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Book cover Progress in Mathematics

Part of the book series: Progress in Mathematics ((PM,volume 9))

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Abstract

The present survey includes papers reviewed in the “Mathematics” section of Referativnyi Zhurnal from October 1962 to October 1967. During the period indicated there was a sharp increase in the number of publications on various aspects of category theory: the previous survey [17] comprised about 40 papers, while now there are more than two hundred. The authors have done their best to pinpoint the directions of research which in their opinion are becoming consolidated and to illuminate in more detail the fundamental papers in each direction; at the same time, certain papers are mentioned only in the Literature Cited section. On the other hand, the extensive group of papers by Ehresmann [70–107] on categories of structured structures is almost not at all reflected in this survey for two main reasons: first, the too-free use of the concept of class has not received wide support in the literature; second, the large number of awkward definitions makes it impossible to present EhresmamVs results within the scope of this article; the interested reader can refer to Ehresmann’s book [95].

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Literature Cited

  1. G. D. Berishvili, “Direct and inverse limits,” Soobshch. Akad. Nauk GruzSSR, 43(3): 535–542 (1966).

    MATH  Google Scholar 

  2. G. Kh. Berman, “Functors in the category of locally convex spaces,” Dokl. Akad. Nauk SSSR, 154(3): 497–499 (1964).

    MathSciNet  Google Scholar 

  3. I. E. Burmistrovich, “Embedding of an additive category into a category with direct products,” Dokl. Akad. Nauk SSSR, 132(6): 1235–1237 (1960).

    Google Scholar 

  4. I. M. Gel’fand and G. E. Shilov, “Categories of finite-dimensional spaces,” Vestn. Mosk. Univ., Mat., Mekh., No. 4, 27–48 (1963).

    Google Scholar 

  5. N. I. Glebov, “The structure of the class of R-tests for equivalence,” in: Problems of Cybernetics, No. 9, Fizmatgiz, Moscow (1963), pp. 103–122.

    Google Scholar 

  6. A. Grothendieck, “Sur quelques points d’algebre homologique,” Tohoku Math. J., 9:119–221 (1957).

    MathSciNet  MATH  Google Scholar 

  7. Kh. N. Inasaridze, “On the theory of extensions in categories,” Soobshch. Akad. Nauk GruzSSR, 30(5): 537–544 (1963).

    MathSciNet  MATH  Google Scholar 

  8. Kh. N. Inasaridze, “Universal functors,” Soobshch. Akad. Nauk GruzSSR, 38(3): 513–520 (1965).

    MathSciNet  MATH  Google Scholar 

  9. L. M. Kissina and A. S. Shvarts, “On the description of duality of functors,” Dokl. Akad. Nauk SSSR, 167(2): 282–285 (1966).

    MathSciNet  Google Scholar 

  10. V. V. Kuznetsov, “Duality of functors in the category of sets with base points,” Dokl. Akad. Nauk SSSR, 159(4): 738–741 (1964).

    MathSciNet  MATH  Google Scholar 

  11. A. G. Kurosh, “Radicals of rings and algebras,” Mat. Sb., 33(1): 13–26 (1953).

    Google Scholar 

  12. A. G. Kurosh, “Direct decompositions in algebraic categories,” Tr. Mosk. Mat. Obshch., Vol. 8, pp. 391–412 (1959); Vol. 9, p. 562 (1960).

    Google Scholar 

  13. A. G. Kurosh, “Radicals in group theory,” Sibirsk. Mat. Zh., 3(6): 912–931 (1962).

    MATH  Google Scholar 

  14. A. G. Kurosh, A. Kh. Livshits, and E. G. Shurgeifer, “Foundations of the theory of categories,” Usp. Mat. Nauk, 15(6): 3–52 (1960).

    Google Scholar 

  15. A. Kh. Livshits, “Summation of mappings and the concept of a center in categories,” Mat. Sb., 60(2): 159–184 (1963).

    MathSciNet  Google Scholar 

  16. A. Kh. Livshits, “Category-theoretical foundations of duality, radicality, and semisimplicity,” Sibirsk. Mat. Zh., 5(2): 319–336 (1964).

    MATH  Google Scholar 

  17. A. Kh. Livshits, M. S. Tsalenko, and E. G. Shul’geifer, “Category theory,” in: Algebra. Topology. 1962, Progress in Science, VINITI Akad. Nauk SSSR, Moscow (1963), pp. 90–106.

    Google Scholar 

  18. A. Kh. Livshits, M. S. Tsalenko, and E. G. Shul’geifer, “Varieties in categories,” Mat. Sb., 63(4): 554–581 (1964).

    MathSciNet  Google Scholar 

  19. S. MacLane, Homology, Springer-Verlag, Berlin (1963), 422 pp.

    Book  MATH  Google Scholar 

  20. A. I. Mal’tsev, “Determining relations in categories,” Dokl. Akad. Nauk SSSR, 119(6): 1095–1098 (1958).

    MathSciNet  MATH  Google Scholar 

  21. B. S. Mityagin and A. S. Shvarts, “Functors in categories of Banach spaces,” Usp. Mat. Nauk, 19(2): 65–130 (1964).

    MATH  Google Scholar 

  22. A. Pultr and Z. Hedrlin, “The representation of small categories,” Dokl. Akad. Nauk SSSR, 160(2): 284–286 (1965).

    MathSciNet  Google Scholar 

  23. Yu. M. Ryabukhin, “Radicals in categories,” Izv. Akad. Nauk MoldSSR, Ser. Fiz.-Mat. i Tekhn. Nauk, No. 6, 58–74 (1964).

    Google Scholar 

  24. V. Trnkova, “On the theory of categories,” Comment. Math. Univ. Carolinae, 3(4): 9–35 (1962).

    MathSciNet  Google Scholar 

  25. D. B. Fuks, “Homotopy duality,” Dokl. Akad. Nauk SSSR, 141(4): 818–821 (1961).

    MathSciNet  Google Scholar 

  26. D. B. Fuks, “Natural mappings of functors in the category of topological spaces,” Mat. Sb., 62(2): 160–179 (1963).

    MathSciNet  Google Scholar 

  27. D. B. Fuks and A.S. Shvarts, “On the homotopy theory of functors in the category of topological spaces,” Dokl. Akad. Nauk SSSR, 143(3): 543–546 (1962).

    MathSciNet  Google Scholar 

  28. A. Ya. Khelemskii, “Algebras of nilpotent operators and the categories connected with them,” Vestn. Mosk. Univ., Mat., Mekh., No. 4, 49–55 (1963).

    Google Scholar 

  29. M. S. Tsalenko, “Proper unions and special subdirect sums in categories,” Mat. Sb., 57(1): 75–94 (1962).

    MathSciNet  Google Scholar 

  30. M. S. Tsalenko, “The completion of categories by free and direct unions of objects,” Mat. Sb., 60(2): 235–256 (1963).

    MathSciNet  Google Scholar 

  31. M. S. Tsalenko, “Correspondences over a quasiexact category,” Dokl. Akad. Nauk SSSR, 155(2): 292–294 (1964).

    MathSciNet  Google Scholar 

  32. M. S. Tsalenko, “R-complete subcategories of the category of groups,” Usp. Mat. Nauk, 21(1): 174–175 (1966).

    Google Scholar 

  33. A. S. Shvarts, “Duality of functors,” Dokl. Akad. Nauk SSSR, 148(2): 288–291 (1963).

    MathSciNet  Google Scholar 

  34. E. G. Shul’geifer, “On the general theory of radicals in categories,” Mat. Sb., 51(4): 487–500 (1960).

    MathSciNet  Google Scholar 

  35. E. G. Shul’geifer, “Proper embeddings of categories,” Usp. Mat. Nauk, 17(3): 212–213 (1962).

    Google Scholar 

  36. E. G. Shul’geifer, “Proper embeddings of categories,” Mat. Sb., 61(4): 467–503 (1963).

    MathSciNet  Google Scholar 

  37. E. G. Shul’geifer, “The structure of the ideals of an object of a category. II,” Mat. Sb., 62(3): 335–344 (1963).

    MathSciNet  Google Scholar 

  38. E. G. Shul’geifer, “Functorial characterization of strict radicals in categories,” Sibirsk. Mat. Zh., 7(6): 1412–1421 (1966).

    Google Scholar 

  39. J. M. Adams, “Abstract homotopy theory in categories,” Doctoral dissertation, New Mexico State University, 1963, 35 pp. Dissertation Abstr., 24(4): 1625 (1963).

    Google Scholar 

  40. S. A. Amitsur, “A general theory of radicals. II,” Am. J. Math, 76:100–125 (1954).

    Article  MathSciNet  MATH  Google Scholar 

  41. P.C. Baayen, “Opmerkingen over Kowalsky’s artikel: ‘Kategorien topolo-gischer Räume’,” Rapp. Math. Centrum., No. 14, p. 6 (1962).

    Google Scholar 

  42. L. Badescu, “Functori Adjuncti Contravarianti,”Studii Si Cercetǎri Mat. Acad. RSR, 17(7): 1145–1152 (1965).

    MathSciNet  MATH  Google Scholar 

  43. L. Badescu, “Extension de la definit on des foncteurs derives pour les categories abeliennes,” Rev. Roumaine Math. Pures et Appl., 11(1): 103–107 (1966).

    MathSciNet  Google Scholar 

  44. C. Bǎnicǎ and N. Popescu, “Quelques considerations sur l’exactitude des foncteurs,” Bull. Math. Soc. Sci. Math. et Phys. (RPR), 7(3–4): 143–147 (1963).

    Google Scholar 

  45. C. Bǎnicǎ and N. Popescu, “Sur les catégories préabeliennes,” Rev. Roumaine Math. Pures, et Appl. (RPR), 10(5): 621–633 (1965).

    Google Scholar 

  46. C. Bǎnicǎ and N. Popescu, “Asupra categoriilor preabeliene,” Studii Si Cercetǎri Mat. Acad. RSR, 17(4): 563–575 (1965).

    Google Scholar 

  47. L. Bégueri and G. Poitou, “‘Diagram-chasing’ dans les catégories abéliennes,” Bull. Soc. Math. France, 93(4): 323–332 (1965).

    MathSciNet  MATH  Google Scholar 

  48. J. Benabou, “Catégories avec multiplication,” Compt. Rend. Acad. Sci., 256(9):1887–1890 (1963).

    MathSciNet  MATH  Google Scholar 

  49. J. Benabou, “Algèbre élémentaire dans les catégories avec multiplication,” Compt. Rend. Acad. Sci., 258(3): 771–774 (1964).

    MathSciNet  MATH  Google Scholar 

  50. J. Benabou, “Catégories relatives,” Compt. Rend. Acad. Sci., 260(14): 3824–3827 (1965).

    MathSciNet  MATH  Google Scholar 

  51. P. Boero, “Categorie omologiche,” Rend. Semin. Mat. Univ. Padova, 35(2): 267–298 (1965).

    MathSciNet  MATH  Google Scholar 

  52. R. Bonyun, “On the square of a homological monoid,” Can. Math. Bull., 9(1): 49–55 (1966).

    Article  MathSciNet  MATH  Google Scholar 

  53. J. Braconnier, “Les catégories,” Cahiers Rhodaniens, No. 10, pp. 1/1–1/12 (1961).

    Google Scholar 

  54. J. Bucur, “Fonctions définies sur le spectre d’une catégorie et théories de décompositions,” Rev. Roumaine Math. Pures et Appl. (RPR), 9(6): 583–588 (1964).

    MathSciNet  MATH  Google Scholar 

  55. L. Bukovsky, Z. Hedrlin, and A. Pultr, “On topological representation of semigroups and small categories,” Mat.-Fyz. Casop., 15(3): 197–199 (1965).

    MathSciNet  Google Scholar 

  56. W. Burgess, “The meaning of mono and epi in some familiar categories,” Can. Math. Bull., 8(6): 759–769 (1965).

    Article  MathSciNet  MATH  Google Scholar 

  57. P. Dedecker and J. Mersch., “Précatégories et relations d’équivalence dans les catégories,” Compt. Rend. Acad. Sci., 256(23): 4811–4814 (1963).

    MathSciNet  MATH  Google Scholar 

  58. S. E. Dickson, “A torsion theory for Abelian categories,” Trans. Am. Math. Soc, 121(1): 223–235 (1966).

    Article  MATH  Google Scholar 

  59. H. P. Doctor, “The categories of Boolean lattices, Boolean rings, and Boolean spaces,” Can. Math. Bull, 7(2): 245–252 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  60. K. Drbohlav, “A note on epimorphisms in algebraic categories,” Comment. Math. Univ. Carolinae, 4(2): 81–85 (1963).

    MathSciNet  MATH  Google Scholar 

  61. K. Drbohlav, “Concerning representations of small categories,” Comment. Math. Univ. Carolinae, 4(4): 147–151 (1963).

    MathSciNet  MATH  Google Scholar 

  62. K. Drbohlav, “A categorical generalization of a theorem of G. Birkhoff on primitive classes of universal algebras,” Comment. Math. Univ. Carolinae, 6(1): 21–41 (1965).

    MathSciNet  MATH  Google Scholar 

  63. L. Dubikajtis and J. Iwanski, “An independent system of axioms defining the Ehresmann groupoid,” Bull. Acad. Polon. Sci., Ser. Sci. Math. Astron. et Phys., 12(111): 687–693 (1964).

    MathSciNet  MATH  Google Scholar 

  64. A. Duma, “Asupra categoriilor de diagrame,” Studii Si Cercetǎri Mat. Acad. RSR, 17(5): 803–807 (1965).

    MathSciNet  MATH  Google Scholar 

  65. A. Duma, “Sur les catégories des diagrammes,” Rev. Roumaine Math. Pures et Appl. (RPR), 10(5): 653–657 (1965).

    MathSciNet  Google Scholar 

  66. B. Eckmann and P. J. Hilton, “Grouplike structures in general categories. I,” Math. Ann., 145(3): 227–255 (1962).

    Article  MathSciNet  MATH  Google Scholar 

  67. B. Eckmann and P. J. Hilton, “Grouplike structures in general categories. II,” Math. Ann., 151(2): 150–186 (1963).

    Article  MathSciNet  MATH  Google Scholar 

  68. B. Eckmann and P. J. Hilton, “Grouplike structures in general categories. HI,” Math. Ann., 150(2): 165–187 (1963).

    Article  MathSciNet  Google Scholar 

  69. B. Eckmann and H. Kleisli, “Algebraic homotopy groups and Frobenius algebras. HI,” J. Math., 6(4): 533–552 (1962).

    MathSciNet  MATH  Google Scholar 

  70. C. Ehresmann, “Catégories inductives et pseudogroupes,” Ann. Inst. Fourier, Vol. 10, pp. 307–332 (1960).

    Article  MathSciNet  MATH  Google Scholar 

  71. C. Ehresmann, “Especes des structures locales,” Semin. Topol. et Geom. Different., Fac. Sci. Paris, Vol. 3, pp. 1–24 (1960–1962).

    Google Scholar 

  72. C. Ehresmann, “Elargissements des categories,” Semin. Topol. et Geom. Différent., Fac. Sci. Paris, Vol. 3, pp. 25–73 (1960–1962).

    Google Scholar 

  73. C. Ehresmann, “Catégories des foncteurs types,” Rev. Union. Math. Argent, y Asoc. Fis. Argent, Vol. 20, pp. 194–209 (1962).

    MathSciNet  MATH  Google Scholar 

  74. C. Ehresmann, “Catégories structurées, III. Quintettes et applications covari-antes,” Cahiers Semin. Topol. et Géom. Différent., Fac. Sci. Paris, Vol. 5 (1963).

    Google Scholar 

  75. C. Ehresmann, “Catégories structurées quotients,” Cahiers Semin. Topol. et Geom. Différent., Fac. Sci. Paris, Vol. 5 (1963).

    Google Scholar 

  76. C. Ehresmann, “Prolongements des catégories différentiables,” Cahiers Semin. Topol. et Geom. Différent., Fac. Sci. Paris, Vol. 6 (1964).

    Google Scholar 

  77. C. Ehresmann, “Catégories doubles et catégories structurées.” Compt. Rend. Acad. Sci., 256(6): 1198–1201 (1963).

    MathSciNet  MATH  Google Scholar 

  78. C. Ehresmann, “Catégorie double des quintettes; applications covariantes,” Compt. Rend. Acad. Sci., 256(9): 1891–1894 (1963).

    MathSciNet  MATH  Google Scholar 

  79. C. Ehresmann, “Catégories structurées d’operateurs,” Compt. Rend. Acad. Sci., 256(10): 2080–2083 (1963).

    MathSciNet  MATH  Google Scholar 

  80. C. Ehresmann, “Sous-structures et applications K-covariantes,” Compt. Rend. Acad. Sci., 256(11): 2280–2283 (1963).

    MathSciNet  MATH  Google Scholar 

  81. C. Ehresmann, “Structures quotients et catégories quotients,” Compt. Rend. Acad. Sci., 256(24): 5031–5034 (1963).

    MathSciNet  MATH  Google Scholar 

  82. C. Ehresmann, “Catégories structurées,” Ann. Sci. Ecole Norm. Supér., 80(4): 349–426 (1963).

    MathSciNet  MATH  Google Scholar 

  83. C. Ehresmann, “Groupoides sous-inductifs,” Ann. Inst. Fourier, 13(2): 1–60 (1963).

    Article  MathSciNet  MATH  Google Scholar 

  84. C. Ehresmann, “Complétion des catégories ordonnées,” Compt. Rend. Acad. Sci., 257(26): 4110–4113 (1963).

    MathSciNet  MATH  Google Scholar 

  85. C. Ehresmann, “Catégories et structures: Extraits,” Cahiers Semin. Topol. et Géom. Différent., Fac. Sci. Paris, Vol. 6 (1964).

    Google Scholar 

  86. C. Ehresmann, “Structures quotients,” Comment. Math. Helv., 38(3): 219–242 (1964).

    MathSciNet  MATH  Google Scholar 

  87. C. Ehresmann, “Structures quotients,” Comment. Math. Helv., 38(4): 243–283 (1964).

    MathSciNet  Google Scholar 

  88. C. Ehresmann, “Catégories ordonnées, holonomie et cohomologie,” Ann. Inst. Fourier, 14(1): 205–268 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  89. C. Ehresmann, “Complétion des catégories ordonnées,” Ann. Inst. Fourier, 14(2): 89–144 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  90. C. Ehresmann, “Sous-structures et catégories ordonnées,” Fundam. Math., 54(2): 211–228 (1964).

    MathSciNet  MATH  Google Scholar 

  91. C. Ehresmann, “Produit croisé des catégories,”Compt. Rend. Acad. Sci., 258(9): 2461–2464(1964).

    MathSciNet  MATH  Google Scholar 

  92. C. Ehresmann, “Completion des catégories sous-prélocales,” Compt. Rend. Acad. Sci., 259(4): 701–704 (1964).

    MathSciNet  MATH  Google Scholar 

  93. C. Ehresmann, “Expansion d’homomorphismes et foncteurs,” Compt. Rend. Acad. Sci., 259(7): 1372–1375 (1964).

    MathSciNet  MATH  Google Scholar 

  94. C. Ehresmann, “Sur une notion générale de cohomologie,” Compt. Rend. Acad. Sci., 259(13): 2050–2053 (1964).

    MathSciNet  MATH  Google Scholar 

  95. C. Ehresmann, “Catégories et structures,” Dunod, Paris (1965), 358 pp.

    Google Scholar 

  96. C. Ehresmann, “Structures quasiquotients,” Cahiers Semin. Topol. et Géom. Différent., Fac. Sci. Paris, Vol. 7, Oct.(1965).

    Google Scholar 

  97. C. Ehresmann, “Expansion générale des foncteurs,” Compt. Rend. Acad. Sci., 260(1): 30–33 (1965).

    MathSciNet  MATH  Google Scholar 

  98. C. Ehresmann, “Catégorie quotient d’une catégorie par une sous-catégorie,” Compt. Rend. Acad. Sci., 260(8): 2116–2119 (1965).

    MathSciNet  MATH  Google Scholar 

  99. C. Ehresmann, “Quasi-surjections et structures quasi-quotient,” Compt. Rend. Acad. Sci., 261(7): 1577–1580 (1965).

    MathSciNet  MATH  Google Scholar 

  100. C. Ehresmann, “Quasi-catégories structurées,” Compt. Rend. Acad. Sci., 261(9): 1932–1935(1965).

    MathSciNet  MATH  Google Scholar 

  101. C. Ehresmann, “Groupoides structurés quasi-quotient et quasicohomologie,” Compt. Rend. Acad. Sci., 261(22): 4583–4586 (1965).

    MathSciNet  MATH  Google Scholar 

  102. C. Ehresmann, “Expansion des systèmes des structures dominés,” Compt. Rend. Acad. Sci., AB262(1): A8–A11 (1966).

    MathSciNet  Google Scholar 

  103. C. Ehresmann, “Adjonction des limites aux catégories structurées,” Compt. Rend. Acad. Sci., 263(19): A655–A658 (1966).

    MathSciNet  Google Scholar 

  104. C. Ehresmann, “Quasi-élargissement d’un système des structures structurés,” Compt. Rend. Acad. Sci., 263(21): A762–A765 (1966).

    MathSciNet  Google Scholar 

  105. C. Ehresmann, “Premier théorème d’expansion structurée,” Compt. Rend. Acad. Sci., 263(23):A863–A866 (1966).

    MathSciNet  Google Scholar 

  106. C. Ehresmann, “Théorème de quasi-expansion régulière,” Compt. Rend. Acad. Sci., 264(2):A56–A59 (1967).

    MathSciNet  Google Scholar 

  107. C. Ehresmann, “Problèmes universels relatifs aux catégories n-aires,” Compt. Rend. Acad. Sci., 264(6):A273–A276 (1967).

    MathSciNet  Google Scholar 

  108. S. Eilenberg and J. C. Moore, “Adjoint functors and triples. III,” J. Math., 9(3): 381–398 (1965).

    MathSciNet  MATH  Google Scholar 

  109. D. B. A. Epstein, “Functors between tensored categories,” Invent. Math., 1(3): 221–228 (1966).

    Article  MathSciNet  MATH  Google Scholar 

  110. M. Evrard, “Homologie dans les catégories nonabéliennes; exactitude dans C,” Compt. Rend. Acad. Sci., 260(3): 749–751 (1965).

    MathSciNet  MATH  Google Scholar 

  111. M. Evrard, “Homologie dans les catégories nonabéliennes; définition de rhomologie,” Compt. Rend. Acad. Sci., 260(4): 1049–1051 (1965).

    MathSciNet  MATH  Google Scholar 

  112. C. Faith, “A general Wedderburn theorem,” Bull. Am. Math. Soc, 73(1): 65–67 (1967).

    Article  MathSciNet  MATH  Google Scholar 

  113. A. U. Fregoso, “Local categories,” Doctoral Dissertation, Indiana University, 1963, 59 pp. Dissertation Abstr., 25(1): 495 (1964).

    Google Scholar 

  114. A. Frei, “Objets libres dans une catégorie primitive et comultiplications,” Compt. Rend. Acad. Sci., AB262(8): A421–A424 (1966).

    MathSciNet  Google Scholar 

  115. P. Freyd, “Relative homological algebra made absolute,” Proc. Nat. Acad. Sci. USA, 49(1): 19–20(1963).

    Article  MathSciNet  MATH  Google Scholar 

  116. P. Freyd, “Abelian categories: An introduction to the theory of functors,” Harper and Bros., New York (1964), 164 pp.

    MATH  Google Scholar 

  117. P. Freyd, “Algebra-valued functors in general and tensor products in particular,” Colloq. Math., Vol. 14, pp. 89–106 (1964).

    MathSciNet  Google Scholar 

  118. P. Gabriel, “Des catégories abéliennes,” Bull. Soc. Math. France, 90(3): 323–448 (1962).

    MathSciNet  MATH  Google Scholar 

  119. P. Gabriel and U. Oberst, “Spektralkategorien und reguläre Ringe im Von-Neu-mannschen Sinn,” Math. Z., 92(5):389–395 (1966).

    Article  MathSciNet  MATH  Google Scholar 

  120. G. Gemignani, “Gruppi e cogruppi in una categoria,” Ann. Scuola Norm. Super. Pisa. Sci. Fis. e Mat., 20(1): 139–171 (1966).

    MathSciNet  MATH  Google Scholar 

  121. R. Goblot, “Foncteur de séparation,” Compt. Rend. Acad. Sci., AB262(19): A1034–A1036 (1966).

    MathSciNet  Google Scholar 

  122. E. M. Goldberg, “Relations in categories,” Doctoral Dissertation, Columbia University, 1965, 77 pp. Dissertation Abstr., 26(5): 2775–2776 (1965).

    Google Scholar 

  123. J. W. Gray, “Sheaves with values in a category,” Topology, 3(1): 1–18 (1965).

    Article  MathSciNet  MATH  Google Scholar 

  124. M. Hacque, “Satellites des foncteurs limites projéctives et cohomologie abélienne des petites catégories,” Compt. Rend. Acad. Sci., 260(6): 1532–1535 (1965).

    MathSciNet  MATH  Google Scholar 

  125. M. Hasse, “Über Erzeugendensysteme schlichter Kategorien,” Wiss. Z. Techn. Univ. Dresden, 13(4): 1035–1036 (1964).

    MathSciNet  MATH  Google Scholar 

  126. M. Hasse and L. Michler, “Über die Einbettbarkeit von Kategorien in Gruppoide,” Math. Nachr., 25(3): 169–177 (1963).

    Article  MathSciNet  MATH  Google Scholar 

  127. P. J. Hilton, “Note on free and direct products in general categories,” Bull. Soc. Math. Belg., 13(1–2): 38–49 (1961).

    MathSciNet  MATH  Google Scholar 

  128. P. J. Hilton and W. Ledermann, “Remark on the I.c.m. in a homological ring-oid,” Quart. J. Math., 11(44): 287–294 (1960).

    Article  MathSciNet  MATH  Google Scholar 

  129. M. Hocquemiller, “Probléme universel de catégorie,” Bol. Soc. Mat. São Paulo, 18(1–2): 49–55 [1963 (1966)].

    Google Scholar 

  130. H.-J. Hoehnke, “Einige Bemerkungen zur Einbettbarkeit von Kategorien in Gruppoide,” Math. Nachr., 25(3): 179–190 (1963).

    Article  MathSciNet  MATH  Google Scholar 

  131. H.-J. Hoehnke, “Zur Theorie der Gruppoide. IX,” Monatsber. Dtsch. Akad. Wiss. Berlin, 5(7): 405–411 (1963).

    MathSciNet  MATH  Google Scholar 

  132. F. Hoffmann, “Über eine die Kategorie der Gruppen umfassende Kategorie,” Sitzsber. Bayer. Acad. Wiss. Math.-Naturwiss. Kl., 1960, Munich (1961), pp. 163–204.

    Google Scholar 

  133. P. J. Huber, “Homotopy theory in general categories,” Math. Ann., 144(5): 361–385(1961).

    Article  MathSciNet  MATH  Google Scholar 

  134. P. J. Huber, “Standard constructions in Abelian categories,” Math. Ann., 146(4): 321–325 (1962).

    Article  MathSciNet  MATH  Google Scholar 

  135. M. Husek, “S-categories,” Comment. Math. Univ. Carolinae, 5(1): 37–46 (1964).

    MathSciNet  MATH  Google Scholar 

  136. M. Husek, “Remarks on reflections,” Comment. Math. Univ. Carolinae, 7(2): 249–253 (1966).

    MathSciNet  MATH  Google Scholar 

  137. J. R. Isbell, “Adequate subcategories,” Ill. J. Math., 4(4): 541–552 (1960).

    MathSciNet  MATH  Google Scholar 

  138. J. R. Isbell, “Two set-theoretical theorems in categories,” Fundam. Math., 53(1): 43–49(1963).

    MathSciNet  MATH  Google Scholar 

  139. J. R. Isbell, “Subobjects, adequacy, completeness, and categories of algebras,” Rozpr. Mat., No. 36, 33 pp (1964).

    MathSciNet  Google Scholar 

  140. J. R. Isbell, “Natural sums and abelianizing,” Pacif. J. Math., 14(4): 1265–1281 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  141. E. J. Javier, “Categorias de semigrupos principales,” Rev. Mat. Hisp.-Amer., 24(6): 207–217 (1964).

    MathSciNet  Google Scholar 

  142. E. J. Javier, “Una categoria de semigrupos,” Acta Salmanticensia, Ser. Cienc, 6(4): 79–88 (1965).

    Google Scholar 

  143. G. Joubert, “Extensions de foncteurs ordonnés,” Compt. Rend. Acad. Sci., 260(12): 3251–3254 (1965).

    MathSciNet  MATH  Google Scholar 

  144. G. Joubert, “Extensions des foncteurs ordonnés et applications,” Compt. Rend. Acad. Sci., 261(3): 623–626 (1965).

    MathSciNet  MATH  Google Scholar 

  145. M. Jurchescu and A. Lascu, “Morfisme stricte, categorii cantoriene, functori de completare,” Studii Si Cercetǎri Mat. Acad. RSR, 18(2): 219–234 (1966).

    MathSciNet  MATH  Google Scholar 

  146. P.-F. Jurie, “Sur quelques caractérisations des sommes amalgamées d’homo-morphismes bpp-éiens, “ Compt. Rend. Acad. Sci., 264(5):A217–A220 (1967).

    MathSciNet  Google Scholar 

  147. L. Kauffman, “Categories,” Tech. Engng. News, 47(8): 41–43 (1966).

    Google Scholar 

  148. G. M. Kelly, “On the radical of a category,” J. Austral. Math. Soc, 4(3): 299–307 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  149. G. M. Kelly, “Complete functors in homology. I. Chain maps and endomorphisms,” Proc. Cambridge Phil. Soc, 60(4): 721–735 (1964).

    Article  MATH  Google Scholar 

  150. G. M. Kelly, “Complete functors in homology. II. The exact homology sequence,” Proc. Cambridge Phil. Soc, 60(4): 737–749 (1964).

    Article  Google Scholar 

  151. G. M. Kelly, “Tensor products in categories,” J. Algebra, 2(1): 15–37 (1965).

    Article  MathSciNet  MATH  Google Scholar 

  152. G. M. Kelly, “On MacLane’s conditions for coherence of natural associativities, commutativities, etc,” J. Algebra, 1(4): 397–402 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  153. J. F. Kennison, “Reflective functors in general topology and elsewhere,” Trans. Am. Math. Soc, 118(6):303–315 (1965).

    Article  MathSciNet  MATH  Google Scholar 

  154. H. Kleisli, “Homotopy theory in Abelian categories,” Can. J. Math., 14(1): 139–169(1962).

    Article  MathSciNet  MATH  Google Scholar 

  155. H. Kleisli, “Every standard construction is induced by a pair of adjoint functors,” Proc. Am. Math. Soc, 16(3): 544–546 (1965).

    Article  MathSciNet  MATH  Google Scholar 

  156. Lam Tsit-Yuen, “The category of Noetherian modules,” Proc Nat. Acad. Sci. USA, 55(5): 1038–1040 (1966).

    Article  Google Scholar 

  157. G. B. Lampton, Jr., “Abstract Abelian categories,” Doctoral Dissertation, University of South Carolina, 1964, 67 pp. Dissertation Abstr., 25(11): 6658 (1965).

    Google Scholar 

  158. M. L. Laplaza, “Nota sobre los epimortismos en la categoria de los anillos,” Rev. Mat. Hisp.-Amer., 26(3): 67–72 (1966).

    MathSciNet  MATH  Google Scholar 

  159. R. Lavendhomme, “La notion d’idéal dans la théorie des catégories,” Ann. Soc. Sci. Bruxelles, Ser. 1, 79(1): 5–25 (1965).

    MathSciNet  Google Scholar 

  160. R. Lavendhomme, “Un plongement pleinement fidèle de la catégorie des groups. Application à l’algébrehomologique nonabelienne,” Bull. Soc. Math. Belg., 17(2): 153–185 (1965).

    MathSciNet  MATH  Google Scholar 

  161. F. W. Lawvere, “Functorial semantics of algebraic theories,” Proc Nat. Acad. Sci., 50(5): 869–872 (1963).

    Article  MathSciNet  MATH  Google Scholar 

  162. F. W. Lawvere, “An elementary theory of the category of sets,” Proc. Nat. Acad. Sci. USA, 52(6): 1506–1511 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  163. P. Lecouturier, “Quelques propriétés des catégories hofmanniennes,” Ann. Soc. Sci. Bruxelles, Ser. 1, 80(1): 19–72 (1966).

    MathSciNet  MATH  Google Scholar 

  164. S. Legrand, “Construction des catégories ordonnées, projections de graphes multiplicatifs ordonnés,” Compt. Rend. Acad. Sci., 260(12): 3255–3258 (1965).

    MathSciNet  MATH  Google Scholar 

  165. S. Legrand, “Catégorie double projection d’un graphe multiplicatif double,” Compt. Rend. Acad. Sci., AB262(7): A381–A383 (1966).

    MathSciNet  Google Scholar 

  166. J. B. Leicht, “On commutative squares,” Can. J. Math., 15(1): 59–79 (1963).

    Article  MathSciNet  MATH  Google Scholar 

  167. J. B. Leicht, “Über die elementaren Lemmata der homologischen Algebra in quasiexacten Kategorien,” Monatsh. Math., 68(3): 240–254 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  168. J. Levy-Bruhl, “Sur les catégories ordonnées,” Compt. Rend. Acad. Sci., 258(6): 1669–1671 (1964).

    MathSciNet  MATH  Google Scholar 

  169. J. Levy-Bruhl, “Demi-groupe et catégorie modulaires,” Compt. Rend. Acad. Sci., 260(15): 4134–4136 (1965).

    MathSciNet  Google Scholar 

  170. J. Levy-Bruhl, “Sur les notions d’image, noyau, coimage, conoyau,” Compt. Rend. Açad. Sci., 262(25): A1381–A1384 (1966).

    MathSciNet  Google Scholar 

  171. F. E. J. Linton, “Autonomous categories and duality of functors,” J. Algebra, 2(3): 315–349 (1965).

    Article  MathSciNet  MATH  Google Scholar 

  172. S. MacLane, “Locally small categories and the foundations of set theory,” in: Infinitistic Methods, Pergamon Press, Oxford; Warszawa. P.W.N. (1961), pp. 25–43.

    Google Scholar 

  173. S. MacLane, “An algebra of additive relations,” Proc. Nat. Acad. Sci. USA, 47(7): 1043–1051 (1961).

    Article  MathSciNet  MATH  Google Scholar 

  174. S. MacLane, “Natural associativity and commutativity,” Rice Univ. Studies, 49(4): 28–46 (1963).

    MathSciNet  MATH  Google Scholar 

  175. S. MacLane, “Categorical algebra,” Bull. Am. Math. Soc, 71(1): 40–106 (1965).

    Article  MathSciNet  MATH  Google Scholar 

  176. J. M. Maranda, “Some remarks on limits in categories,” Can. Math. Bull., 5(2): 133–146 (1962).

    Article  MathSciNet  MATH  Google Scholar 

  177. J. M. Maranda, “Injective structures,” Trans. Am. Math. Soc, 110(1): 98–135 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  178. J. M. Maranda, “Formal categories,” Can. J. Math., 17(5): 758–801 (1965).

    Article  MathSciNet  MATH  Google Scholar 

  179. J. M. Maranda, “Completions of modules and rings,” Trans. Roy. Soc. Canada, Sec. 1–3(3): 271–291 (1965).

    MathSciNet  Google Scholar 

  180. W. Meier, “Beiträge zur algebraischen Homotopietheorie der Moduln,” Diss., Dokt. Math., Eidgenöss. Techn. Hochschule Zürich (1962), 54 pp.

    Google Scholar 

  181. J. Mersch., “Chasses sur les diagrammes des catégories abéliennes,” Bull. Soc Roy. Sci. Liége, 33(7–8): 411–450 (1964).

    MathSciNet  MATH  Google Scholar 

  182. J. Mersch, “Structures quotients,” Bull. Soc. Roy. Sci. Liège, 33(1–2): 45–58 (1964).

    MathSciNet  MATH  Google Scholar 

  183. J. Mersch, “Le problème du quotient dans les catégories,” Mem. Soc Roy. Sci. Liège, Vol. 11, No. 1 (1965).

    Google Scholar 

  184. B. Mitchell, Theory of Categories, Academic Press, New York (1965), 273 pp.

    MATH  Google Scholar 

  185. B. Mitchell, “The full imbedding theorem,” Am. J. Math., 86(3): 619–637 (1964).

    Article  MATH  Google Scholar 

  186. C. Nǎstǎsescu and N. Popescu, “Sur la structure des objets de certaines catégories abéliennes,” Compt. Rend. Acad. Sci., AB262(24): A1295–A1297 (1966).

    Google Scholar 

  187. Y. Nouazé, “Catégories localement de type fini et catégories localement noethériennes,” Compt. Rend. Acad. Sci., 257(4): 823–824 (1963).

    MATH  Google Scholar 

  188. L. Oubina and J. Bosch, “Sous-jacence, union et intersection en catégories,” Compt. Rend. Acad. Sci., 260(9): 2389–2391 (1965).

    MathSciNet  MATH  Google Scholar 

  189. B. Pareigis, “Cohomology of groups in arbitrary categories,” Proc. Am. Math. Soc, 15(5): 803–819 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  190. N. Popescu, “Elemente de teoria fasciculelor. I,” Studii Si Cercetari Mat. Acad. RSR, 18(2): 267–296 (1966).

    MATH  Google Scholar 

  191. N. Popescu, “Elemente de teoria fasciculelor. II,” Studii Si Cercetari Mat. Acad. RSR, 18(3): 407–456 (1966).

    Google Scholar 

  192. N. Popescu and P. Gabriel, “Caractérisation des catégories abéliennes avec générateurs et limites inductives exactes,” Compt. Rend. Acad. Sci., 258(17): 4188–4190(1964).

    Google Scholar 

  193. A. Pultr, “Concerning universal categories,” Comment. Math. Univ. Carolinae, 5(4): 227–239 (1964).

    MathSciNet  MATH  Google Scholar 

  194. R. Pupier, “Sur les décompositions de morphismes dans les catégories à sommes ou à produits fibres,” Compt. Rend. Acad. Sci., 258(26): 6317–6319 (1964).

    MathSciNet  MATH  Google Scholar 

  195. D. Puppe, “Korrespondenzen in abelschen Kategorien,” Math. Ann., 148(1): 1–30 (1962).

    Article  MathSciNet  MATH  Google Scholar 

  196. J. Riquet, “Categorisation de la notion des structures et des structures locales chez N. Bourbaki et C. Ehresmann. I,” Semin. P. Dubreil, M.-L. Dubreil-Jacotin et C. Pisot. Fac. Sci. Paris, 1960–1961, 14 Annee, Fasc. I, Paris (1963), pp. 5/01–5/32.

    Google Scholar 

  197. P. Robert, “Méthodes fonctionnelles sur l’axiomatique des systèmes de générateurs, des rangs, etc.,” Compt. Rend. Acad. Sci., 260(16): 4291–4294 (1965).

    MATH  Google Scholar 

  198. P. Robert, “Méthodes fonctionnelles sur raxiomatique des systèmes de générateurs des rangs,” Compt. Rend. Acad. Sci., 260(18): 4661–4664 (1965).

    MATH  Google Scholar 

  199. P. Robert, “Methodes fonctionnelles sur l’axiomatique des systèmes de générateurs, des rangs, etc.,” Compt. Rend. Acad. Sci., 260(23): 5983–5986 (1965).

    MATH  Google Scholar 

  200. J.-E. Roos, “Introduction à l’étude de la distributivité des foncteurs lim par rapport aux lim dans des catégories des faisceaux (topos),” Compt. Rend. Acad. Sci. 259(5): 969–972 (1964).

    MathSciNet  MATH  Google Scholar 

  201. J.-E. Roos, “Sur la distributivité des foncteurs lim par rapport aux lim dans les catégories des faisceaux (topos),” Compt. Rend., 259(9): 1605–1608 (1964).

    MathSciNet  MATH  Google Scholar 

  202. J.-E. Roos, “Complément à l’étude de la distributivité des foncteurs lim par rapport aux lim dans les catégories des faisceaux (topos),” Compt. Rend. Acad. Sei., 259(11): 1801–1804 (1964).

    MathSciNet  MATH  Google Scholar 

  203. J.-E. Roos, “Caractérisation des catégories qui sont quotients des catégories des modules par des souscatégories bilocalisantes,” Compt. Rend. Acad. Sci., 261(23): 4954–4957 (1965).

    MathSciNet  MATH  Google Scholar 

  204. T. Rosinger, “Une extension de la notion de catégorie Eilenberg — MacLane,” Rev. Roumaine Math. Pures et Appl. (RPR), 9(9): 881–885 (1964).

    MathSciNet  Google Scholar 

  205. T. Rosinger, “O extindere a notiunii de categorie in sens Eilenberg — MacLane,” Studii Si Cercetǎri Mat. Acad. RPR, 16(8): 997–999 (1964).

    MathSciNet  MATH  Google Scholar 

  206. A. Roux, “Objets injectifs et projectifs,” Cahiers Rhodaniens, No. 10, pp. 3/1–3/7(1961).

    Google Scholar 

  207. A. Roux, “Sur une équivalence des catégories abéliermes,” Compt. Rend. Acad. Sci., 258(23): 5566–5568 (1964).

    MathSciNet  MATH  Google Scholar 

  208. A. Roux, “Un théorème de plongement des catégories,” Compt. Rend. Acad. Sci., 258(19): 4646–4647 (1964).

    MathSciNet  MATH  Google Scholar 

  209. R. Rubio, “Sobre los fundamentos de la geometria diferencial,” Casop. Pestov. Mat., 89(3): 278–295 (1964).

    MathSciNet  MATH  Google Scholar 

  210. S. Salvioli and J. Bosch, “Sous-objets quotients et images en catégories,” Compt. Rend. Acad. Sci., 260(8): 2111–2113 (1965).

    MathSciNet  MATH  Google Scholar 

  211. Z. Semadeni, “Free and direct objects,” Bull. Am. Math. Soc, 69(1): 63–66 (1963).

    Article  MathSciNet  MATH  Google Scholar 

  212. Z. Semadeni, “Projectivity, injectivity, and duality,” Rozpr. Mat., No. 35, (1963).

    Google Scholar 

  213. Z. Semadeni, “Free objects in the theory of categories,” Colloq. Math., Vol. 14, pp. 107–110 (1964).

    MathSciNet  Google Scholar 

  214. A. Solian, “A canonical decomposition of additive functors of modules,” Atti Accad. Naz. Lincei. Rend. CI. Sci. Fis., Mat. e Natur., 36(2): 129–135 (1964).

    MathSciNet  MATH  Google Scholar 

  215. A. Solian, “Foncteurs qui conservent les épimorphismes locaux,” Compt. Rend. Acad. Sci., 259(7): 1376–1379 (1964).

    MathSciNet  MATH  Google Scholar 

  216. A. Solian, “Foncteurs qui transforment les épimorphismes locaux en mono-morphismes locaux,” Rev. Roumaine Math. Pures et Appl., (RPR), 11(4): 401–410(1966).

    MathSciNet  MATH  Google Scholar 

  217. J. Sonner, “On the formal definition of categories,” Math. Z., 80(2): 163–176 (1962).

    Article  MathSciNet  MATH  Google Scholar 

  218. J. Sonner, “Universal and special problems,” Math. Z., 82(3): 200–211 (1963).

    Article  MathSciNet  MATH  Google Scholar 

  219. J. Sonner, “Universal solutions and adjoint homomorphisms,” Math. Z., 86(1): 14–20 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  220. R. Stärk, “Nullsysteme in allgemeinen Kategorien,” Diss. Eidgenöss. Techn. Hochschule Zürich. Dokt. Math. Zürich (1963).

    Google Scholar 

  221. A. Suliński, “The Brown-McCoy radical in categories,” Fundam. Math., 59(1): 23–41 (1966).

    MATH  Google Scholar 

  222. J. C. Taylor, “Weak families of maps,” Can. Math. Bull., 8(6): 771–781 (1965).

    Article  MATH  Google Scholar 

  223. P. Tondeur, “Categories y functores,” Cursos y Semin. Mat. Univ. Buenos Aires, No. 21 (1965).

    Google Scholar 

  224. V. Trnkova, “Sum of categories with amalgamated subcategory,” Comment. Math. Univ. Carolinae, 6(4): 449–474 (1965).

    MathSciNet  MATH  Google Scholar 

  225. V. Trnkova, “Universal categories,” Comment. Math. Univ. Carolinae, 7(2): 143–206 (1966).

    MathSciNet  MATH  Google Scholar 

  226. R. Vazquez, “Seminario de algebra homologica. Gavillas con valores en categorias,” An. Inst. Mat. Univ. Nac. Autónoma México, Vol. 3, pp. 37–77 (1963).

    MATH  Google Scholar 

  227. I. Vidav, “O kategorijah in funktorjih,” Obz. Mat. in Fiz., 11(1): 1–12 (1964).

    Google Scholar 

  228. W. Waliszewski, “Categories, groupoids, pseudogroups and analytical structures,” Rozpr. Mat., No. 45(1965).

    Google Scholar 

  229. B. Wegener, “Factorgruppoide und homomorphe Abbildungen bei Gruppoiden,” Wiss. Z. Techn. Hochschule Dresden, 10(3): 423–431 (1961).

    MATH  Google Scholar 

  230. M. L. Wheat, “Radical subcategories,” Doctoral Dissertation, University of Kansas, 1964, 68 pp. Dissertation Abstr., 26(2): 1076–1077 (1965).

    Google Scholar 

  231. O. Wyler, “Weakly exact categories,” Arch. Math., 17(1): 9–19 (1966).

    Article  MathSciNet  MATH  Google Scholar 

  232. O. Wyler, “Direct sums in weakly exact categories,” Arch. Math., 17(3): 216–225(1966).

    Article  MathSciNet  MATH  Google Scholar 

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Authors
  1. M. S. Tsalenko
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  2. E. G. Shul’geifer
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  1. V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR, Moscow, Russia

    R. V. Gamkrelidze

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Tsalenko, M.S., Shul’geifer, E.G. (1971). Categories. In: Gamkrelidze, R.V. (eds) Progress in Mathematics. Progress in Mathematics, vol 9. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-3306-7_1

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