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Kan extensions, cotriples and andré (co) homology

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Category Theory, Homology Theory and their Applications II

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 92))

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Bibliography

  1. André, M., Méthode simpliciale en algèbre homologique et algèbre commutative, (Lecture notes in Mathematics, #32), Springer, 1967.

    Google Scholar 

  2. Barr, M. and J. Beck, “Homology and standard constructions”, (to appear in Lecture Notes in Mathematics).

    Google Scholar 

  3. Beck, J., “Triples, algebras and cohomology”, Dissertation, Columbia, (1964–67).

    Google Scholar 

  4. Barr, M. and Beck, J., “Acyclic models and triples”, in: Conference on Categorical Algebra, pp. 336–343, Springer, (1966).

    Google Scholar 

  5. Buchsbaum, D., “Homology and universal functors”, in; (Lecture Notes in Mathematics, #61), Springer, 1968.

    Google Scholar 

  6. Dold, A., “Zur Homotopietheorie der Kettenkomplexe”, Math. Annalen, 140; 278–298, (1960).

    Article  MathSciNet  MATH  Google Scholar 

  7. Dold, A., S. MacLane, U. Oberst, “Projective classes and acyclic models”, in; A. Dold, Heidelberg and Eckmann (eds.), Reports of the Midwest Category Seminar, (Lecture Notes in Mathematics, #47); 78–91, Springer, 1967.

    Google Scholar 

  8. Dold, A. and D. Puppe, “Homologie nicht-additiver Funktoren”, Ann. Inst. Fourier, 11; 291— (1961).

    Article  MathSciNet  MATH  Google Scholar 

  9. Dubuc, E., “Adjoint triangles”, in; (Lecture notes in Mathematics, #61), Springer, 1968.

    Google Scholar 

  10. Fisher, J., “The tensor product of functors, satellites and derived functors', J. of Algebra, to appear.

    Google Scholar 

  11. Freyd, P., Abelian Categories, Harper and Row: New York, 1964.

    MATH  Google Scholar 

  12. Grothendieck, A., “Sur quelques points d'algèbre homologique”, Tôhoku, Math. J., 9; 119–221, (1957).

    MathSciNet  MATH  Google Scholar 

  13. Kan, D., “Adjoint Functors”, Trans. Amer. Math. Soc., 87, 295–329 (1958).

    MathSciNet  MATH  Google Scholar 

  14. Lawvere, F., “Functorial semantics and algebraic theories”, Proc. Nat. Acad. Sci., 50; 869–872, (1963).

    Article  MathSciNet  MATH  Google Scholar 

  15. Linton, F., “Some aspects of equational categories”, in; Conference on Categorical Algebra, pp. 84–94, Springer, (1966).

    Google Scholar 

  16. MacLane, S., Homology, Springer, 1963.

    Google Scholar 

  17. Oberst, U., “Basiserweiterung in der Homologie kleiner Kategorien”, Math. Zeitschrift, 100; 36–58, (1967).

    Article  MathSciNet  MATH  Google Scholar 

  18. Oberst, U., “Homology of categories and exactness of direct limits”, to appear.

    Google Scholar 

  19. Tierney, M., and W. Vogel, “Simplicial resolutions and derived functors”, Mim. Notes, E.T.H., (1968).

    Google Scholar 

  20. Ulmer, F., “Acyclic models and Kan extensions”, this volume.

    Google Scholar 

  21. -, “Representable functors with values in arbitrary categories”, J. of Algebra, 8; 96–129, (1968).

    Article  MathSciNet  MATH  Google Scholar 

  22. Ulmer, F., “Properties of Kan extensions”, Mim. Notes, E.T.H., (1966).

    Google Scholar 

  23. Ulmer, F., “On André and cotriple (co) homology and their relationship to classical homological algebra”, (to appear in Lecture Notes in Mathematics).

    Google Scholar 

  24. Watts, C. E., “A homology theory for small categories”, in; Conference on Categorical Algebra, pp. 331–335, Springer, (1966).

    Google Scholar 

  25. Yoneda, N., “On Ext and exact sequences”, J. Fac. Sci. Tokyo, Sec. I, 8; 507–576, (1961).

    MathSciNet  MATH  Google Scholar 

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Ulmer, F. (1969). Kan extensions, cotriples and andré (co) homology. In: Category Theory, Homology Theory and their Applications II. Lecture Notes in Mathematics, vol 92. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080773

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  • DOI: https://doi.org/10.1007/BFb0080773

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04611-0

  • Online ISBN: 978-3-540-36101-5

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