Review of the elements of 2-categories

  • G. M. Kelly
  • Ross Street
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 420)


Natural Transformation Monoidal Category Left Adjoint Monoidal Functor Vertical Composition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. Benabou, Introduction to bicategories, Lecture Notes in Math. 47 (1967), 1–77.MathSciNetCrossRefGoogle Scholar
  2. [2]
    M.C. Bunge, Bifibration induced adjoint pairs, Lecture Notes in Math. 195 (1971), 70–122.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    M.C. Bunge, Coherent extensions and relational algebras (preprint, March 1973).Google Scholar
  4. [4]
    B.J. Day and G.M. Kelly, Enriched functor categories, Lecture Notes in Math. 106 (1969), 178–191.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    E.J. Dubuc, Kan extensions in enriched category theory,=Lecture Notes in Math. 145 (1970).Google Scholar
  6. [6]
    C. Ehresmann, Catégories structurées, Ann. Sci. École Norm. Sup. 80 (1963), 349–425.MathSciNetzbMATHGoogle Scholar
  7. [7]
    C. Ehresmann, Catégories et structures (Dunod, Paris, 1965).zbMATHGoogle Scholar
  8. [8]
    S. Eilenberg and G.M. Kelly, Closed categories, Proc. Conf. on Categorical Algebra (La Jolla 1965.) (Springer, New York, 1966).CrossRefGoogle Scholar
  9. [9]
    P. Gabriel and F. Ulmer, Lokal präsentierbare Kategorien,=Lecture Notes in Math. 221 (1971).Google Scholar
  10. [10]
    J.W. Gray, The categorical comprehension scheme, Lecture Notes in Math. 99 (1969), 242–312.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    J.W. Gray, Report "The meeting of the Midwest Category Seminar in Zürich, August 24–30, 1970", Lecture Notes in Math. 195 (1971), 248–255.CrossRefzbMATHGoogle Scholar
  12. [12]
    J.W. Gray, Formal category theory, to appear in Lecture Notes in Math.Google Scholar
  13. [13]
    A. Grothendieck, Catégories fibrées et descente, Séminaire de Géométrie Algébrique, Institut des Hautes Études Scientifiques, Paris (1961).Google Scholar
  14. [14]
    G.M. Kelly, Adjunction for enriched categories, Lecture Notes in Math. 106 (1969), 166–177.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    G.M. Kelly, On clubs and doctrines (in this volume).Google Scholar
  16. [16]
    G.M. Kelly, Coherence theorems for lax algebras and for distributive laws (in this volume).Google Scholar
  17. [17]
    G.M. Kelly, Doctrinal adjunction (in this volume).Google Scholar
  18. [18]
    F.W. Lawvere, Ordinal sums and equational doctrines, Lecture Notes in Math. 80 (1969), 141–155.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    F.E.J. Linton, Autonomous categories and duality of functors, Journal of Algebra 2 (1965), 315–349.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    E. Manes, A triple miscellany: some aspects of the theory of algebras over a triple (Dissertation, Wesleyan University, 1967).Google Scholar
  21. [21]
    P.H. Palmquist, The double category of adjoint squares, Lecture Notes in Math. 195 (1971), 123–153.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    J.E. Roberts, A characterization of initial functors, Journal of Algebra 8 (1968), 181–193.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    R. Street, The formal theory of monads, J. Pure and Applied Algebra, 2 (1972), 149–168.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    R. Street, Two constructions on lax functors, Cahiers de Topologie et Géometrie Différentielle XIII, 3 (1972), 217–264.MathSciNetzbMATHGoogle Scholar
  25. [25]
    R. Street, Fibrations and Yoneda's lemma in a 2-category, (in this volume).Google Scholar
  26. [26]
    R. Street, Elementary cosmoi, (in this volume).Google Scholar
  27. [27]
    V. Zöberlein, Doktrinen auf 2-Kategorien (Manuscript, Math. Inst. der Univ. Zürich, 1973).Google Scholar

Copyright information

© Springer-Verleg 1974

Authors and Affiliations

  • G. M. Kelly
  • Ross Street

There are no affiliations available

Personalised recommendations