Applied Categorical Structures

, Volume 4, Issue 2–3, pp 129–136 | Cite as

The development and prospects for category theory

  • Saunders Mac Lane


This paper is a formulation of my personal opinion of the historical development and the present prospects of category theory.

Mathematics Subject Classification (1991)



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Artin, E.: Galois Theory, Notre Dame Mathematical Lectures No. 2, 2nd edn, Notre Dame Univ. Press, 1944.Google Scholar
  2. Artin, M., Grothendieck, A., and Verdier, J. L.: Théorie des topos et cohomologie étale des schémas (SGA 4), Springer Lecture Notes in Math. 269 and 270, 1972; also 305, 1973.Google Scholar
  3. BourbakiNicolas: Eléments de mathématique, livre 1, Théorie des ensembles, Paris, Hermann, 1939.Google Scholar
  4. BrandtH.: Über die Komponierbarkeit quaternärer quadratische Formen, Math. Ann. 94 (1925), 179–197.Google Scholar
  5. BungeM.: Topos theory and Souslin's hypothesis, J. Pure Appl. Alg. 4 (1974), 159–187.Google Scholar
  6. DedekindR.: Über die von drei Moduln erzeugete Dualgruppe, Math. Ann. 53 (1900), 371–443.Google Scholar
  7. EhresmannCh.: Gattungen von lokalen Structuren, Jahresbericht der Deutschen Math. Vereiningung 60 (1957), 49–73.Google Scholar
  8. EilenbergS. and MacLaneS.: General theory of natural equivalences, Trans. Amer. Math. Soc. 58 (1945), 231–294.Google Scholar
  9. EilenbergS. and SteenrodN. E.: Foundations of Algebraic Topology, Princeton Univ. Press, Princeton, NJ, 1952.Google Scholar
  10. EilenbergS. and MacLaneS.: Acyclic models, Am. Journ. Math. 75 (1953), 189–199.Google Scholar
  11. EilenbergS. and ZilberJ. A.: Semisimplicial complexes and singular homology, Ann. Math. 51 (1950), 499–513.Google Scholar
  12. GrothendieckA.: Sur quelques points d'algèbra homologique, Tohoko Math. J. 9 (1957), 119–221.Google Scholar
  13. HilbertD., Grundlagen der Geometrie, 1st edn, B. G. Teubner, Stuttgart, 1989, 12th edn, 1927.Google Scholar
  14. JoyalA. and TierneyM.: Classifying spaces for sheaves of simplicial groupoids, J. Pure Appl. Alg. 89 (1993), 135–161.Google Scholar
  15. KanD. M.: Adjoint functors, Trans. Am. Math Soc. 87 (1958), 294–329.Google Scholar
  16. Kapranov, M. M. and Voevodsky, V. A.: 2-Categories and Zamolodchikov Tetrahedral Equations, Preprint, 1992.Google Scholar
  17. KellyG. M. and MacLaneS.: Coherence in closed categories, J. Pure Appl. Alg. 1 (1971), 97–140.Google Scholar
  18. JoyalA. and StreetR.: Braided tensor categories, Advances in Mathematics 102 (1993), 20–78.Google Scholar
  19. LambekJ. and ScottP. J. Introduction to Higher Order Categorical Logic, Cambridge Univ. Press, Cambridge, U.K., 1988.Google Scholar
  20. LawvereF. W.: An elementary theory of the category of sets, Proc Nat. Acad. Sci. 52 (1964), 1506–1511.Google Scholar
  21. LawvereF. W.: Algebraic theories, algebraic categories and algebraic functors, in Theory of Models, Proc. 1963 Internat. Sympos., Berkeley, North-Holland, Amsterdam, 1965, pp. 413–418.Google Scholar
  22. MacLaneS.: Carnap on logical syntax, Bull Amer. Math. Soc. 44 (1938), 171–176.Google Scholar
  23. MacLaneS.: Groups, categories and duality, Proc. Nat. Acad. Sci. USA 34 (1938), 263–267.Google Scholar
  24. MacLaneS.: Duality for groups, Bull. Amer. Math. Soc. 56 (1950), 485–516.Google Scholar
  25. MacLaneS.: Categories for the Working Mathematician, Springer-Verlag, New York, 1971.Google Scholar
  26. MacLaneS.: Concepts and categories in perspective, in PeterDuren (ed.), A Century of Mathematics in America, Part I, Am. Math. Soc., Providence, RI, 1988, pp. 323–366.Google Scholar
  27. MacLaneS.: Coherence theorems and conformal field theory, in Canadian Mathematical Proceedings, Vol. 13, AMS, Providence, RI, 1992, pp. 321–328.Google Scholar
  28. MacLaneS. and MoedijkI.: Sheaves in Geometry and Logic; A First Introduction to Topos Theory, Springer-Verlag, New York, 1992.Google Scholar
  29. SamuelPierre: On universal mapping and free topological groups, Bull. Am. Math. Soc. 54 (1948), 591–598.Google Scholar
  30. Voreadou, Rodiani: Coherence and commutative diagrams in closed categories, Memoirs Amer. Math. Soc. 9(182) (1977).Google Scholar
  31. Voreadou, R.: A coherence theorem for biclosed categories, Eleutheria 103–150, and 156–187, 1978.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Saunders Mac Lane
    • 1
  1. 1.Department of MathematicsUniversity of ChicagoChicagoU.S.A.

Personalised recommendations