nLab Max Kelly

Gregory Maxwell Kelly (1930-2007) was a category theorist, the founder of the Australian category theory school.

Selected writings

On limits and colimits and exponential objects in the category Top of topological spaces:

On enriched category theory:

  • Max Kelly, Basic Concepts of Enriched Category Theory, Cambridge University Press, Lecture Notes in Mathematics 64 (1982)

    Republished as: Reprints in Theory and Applications of Categories, No. 10 (2005) pp. 1-136 (tac:10, pdf)

On reflective factorization systems:

On Cartesian bicategories:

On monoid objects in monoidal categories:

Publications

  1. Topics in homology theory (PhD Thesis, University of Cambridge, 1957; supervisors S. Wylie and M. G. Barratt).
  2. Single-space axioms for homology theory, Proc. Cambridge Phil. Soc. 55 (1959) 10–22.
  3. The exactness of Čech homology over a vector space, Proc. Cambridge Phil. Soc. 57 (1961) 428–429.
  4. On manifolds containing a submanifold whose complement is contractible, Proc. Cambridge Phil. Soc. 57 (1961) 507–515.
  5. Observations on the Künneth theorem, Proc. Cambridge Phil. Soc. 59 (1963) 575–587.
  6. On the radical of a category, J. Austral. Math. Soc. 4 (1964) 299–307.
  7. Complete functors in homology: I. Chain maps and endomorphisms, Proc. Cambridge Phil. Soc. 60 (1964) 721–735.
  8. Complete functors in Homology: II. The exact homology sequence, Proc. Cambridge Phil. Soc. 60 (1964) 737–749.
  9. On the Mac Lane’s conditions for coherence of natural associativities, commutativities, etc. , J. Algebra 1 (1964) 397–402.
  10. A lemma in homological algebra, Proc. Cambridge Phil. Soc. 61 (1965) 49–52.
  11. Tensor products in categories, J. Algebra 2 (1965) 15–37.
  12. Chain maps inducing zero homology maps, Proc. Cambridge Phil. Soc. 61 (1965), 847–854.
  13. (with S. Eilenberg) A generalization of the functorial calculus, J. Algebra 3 (1966), 366–375.
  14. (with S. Eilenberg) Closed categories, in Proc. Conference on Categorical Algebra (La Jolla, 1965) (Springer-Verlag, Berlin-Heidelberg-New York, 1966) 421–562. Gregory Maxwell Kelly 1930–2007 249
  15. Monomorphisms, epimorphisms, and pullbacks, J. Austral. Math. Soc. 9 (1969) 124–142.
  16. Adjunction for enriched categories, Lecture Notes in Math. 106 (Springer-Verlag, 1969) 166–177.
  17. (with B. J. Day) Enriched functor categories, Lecture Notes in Math. 106 (Springer-Verlag, 1969) 178–191.
  18. (with B. J. Day) On topological quotient maps preserved by pullbacks or products, Proc. Cambridge Phil. Soc. 67 (1970) 553–558.
  19. (with S. E. Dickson) Interlacing methods and large indecomposables, Bull. Austral. Math. Soc. 3 (1970) 337–348.
  20. (with S. Mac Lane) Coherence in closed categories, J. Pure Appl. Algebra 1 (1971) 97–140;Erratum Ibid. 1 (1971) 219.
  21. An Introduction to Algebra and Vector Geometry (Reed Education, Sydney, 1972).
  22. (with P. J. Freyd) Categories of continuous functors I, J. Pure Appl. Algebra 2 (1972) 169–191; Erratum Ibid. 4 (1974) 121.
  23. (with S. Mac Lane) Closed coherence for a natural transformation, Lecture Notes in Math. 281 (Springer-Verlag, 1972) 1–28.
  24. Many-variable functorial calculus I, Lecture Notes in Math. 281 (Springer-Verlag, 1972) 66–105.
  25. An abstract approach to coherence, Lecture Notes in Math. 281 (Springer-Verlag, 1972) 106–147.
  26. A cut-elimination theorem, Lecture Notes in Math. 281 (Springer-Verlag, 1972) 196–213.
  27. Cohérence pour les catégories à distributivité, Cahiers de topologie et géométrie différentielle 14 (1973) 36–37.
  28. (with R. Street) Review of the elements of 2-categories, Lecture Notes in Math. 420 (Springer-Verlag, 1974) 75–103.
  29. On clubs and doctrines, Lecture Notes in Math. 420 (Springer-Verlag, 1974) 181–256.
  30. Doctrinal adjunction, Lecture Notes in Math. 420 (Springer-Verlag, 1974) 257–280.
  31. Coherence theorems for lax algebras and for distributive laws, Lecture Notes in Math. 420 (Springer-Verlag, 1974) 281–375.
  32. (with F. Borceux) A notion of limit for enriched categories, Bulletin Austral. Math. Soc. 12 (1975) 49–72.
  33. Quelques observations sur les demonstrations par récurrence transfinie en algébre catégorique, Cahiers de topologie et géométrie différentielle 16 (1975) 259–263.
  34. (with A. Pultr) On algebraic recognition of direct-product decompositions, J. Pure Appl. Algebra 12 (1978) 207–224.
  35. Saunders Mac Lane and category theory, in Saunders Mac Lane, Selected Papers (Springer-Verlag, New York, Heidelberg, Berlin, 1979) 527–543.
  36. (with F. Foltz and C. Lair) Algebraic categories with few monoidal biclosed structures or none, J. Pure Appl. Algebra 17 (1980) 171–177.
  37. Examples of non-monadic structures on categories, J. Pure Appl. Algebra 18 (1980) 59–66.
  38. (with M. L. Laplaza) Coherence for compact closed categories, J. Pure Appl. Algebra 19 (1980) 193–213.
  39. A unified treatment of transfinite construction for free algebras, free monoids, colimits, associated sheaves, and so on, Bulletin Austral. Math. Soc. 22 (1980) 1–83.
  40. (with V. Koubek) The large limits that all good categories admit, J. Pure Appl. Algebra 22 (1981) 253–263.
  41. Basic Concepts of Enriched Category Theory (London Math. Soc. Lecture Notes Series 64, Cambridge Univ. Press, 1982).
  42. Structures defined by finite limits in the enriched context I, Cahiers de topologie etgéométrie différentielle 23 (1982) 3–42.
  43. On the essentially-algebraic theory generated by a sketch, Bulletin Austral. Math. Soc. 26 (1982) 45–56.
  44. Two addenda to the author’s transfinite constructions article, Bulletin Austral. Math. Soc. 26 (1982) 221–237.
  45. (with S. Kasangian and F. Rossi) Cofibrations and the realization of nondeterministic automata, Cahiers de topologie et géométrie différentielle 24 (1983) 23–46.
  46. (with E. J. Dubuc) A presentation of topoias algebraic relative to categories or graphs, J. Algebra 81 (1983) 420–433.
  47. A note on the generalized reflexion of Guitart and Lair, Cahiers de topologie et géométrie différentielle 24 (1983) 155–159.
  48. (with F. Rossi) Topological categories with many symmetric monoidal closed structures, Bulletin Austral. Math. Soc. 31 (1985) 41–59.
  49. (with C. Cassidy and M. Hébert) Reflective subcategories, localizations and factorization systems, J. Austral. Math. Soc. 38 (Series A) (1985) 287–329; Corrigenda Ibid. 41 (1986) 286.
  50. (with G. B. Im) On classes of morphisms closed under limits, J. Korean Math. Soc. 23 (1986) 1–18.
  51. (with G. B. Im) Some remarks on conservative functors with left adjoints, J. Korean Math. Soc. 23 (1986) 19–33. 250 Historical Records of Australian Science, Volume 21 Number 2
  52. A survey of totality for ordinary and enriched categories, Cahiers de topologie et géométrie différentielle catégoriques 27 (1986) 109–132.
  53. (with G. B. Im) A universal property of the convolution monoidal structure, J. Pure Appl. Algebra 43 (1986) 75–88.
  54. (with F. Borceux) On locales of localizations, J. Pure Appl. Algebra 46 (1987) 1–34.
  55. (with G. B. Im) Adjoint-triangle theorems for conservative functors, Bulletin Austral. Math. Soc. 36 (1987) 133–136.
  56. On the ordered set of reflective subcategories, Bulletin Austral. Math. Soc. 36 (1987) 137–152.
  57. (with M. H. Albert) The closure of a class of colimits, J. Pure Appl. Algebra 51 (1988) 1–17.
  58. (with R. Paré) A note on the Albert-Kelly paper “The closure of a class of colimits”, J. Pure Appl. Algebra 51 (1988) 19–25.
  59. Elementary observations on 2-categorical limits, Bulletin Austral. Math. Soc. 39 (1989) 301–317.
  60. (with R. Blackwell and A. J. Power) Two dimensional monad theory, J. Pure Appl. Algebra 59 (1989) 1–41.
  61. (with F. W. Lawvere) On the complete lattice of essential localizations, Bull. Soc. Math. Belgique 41 (1989) 289–319.
  62. (with G. J. Bird, A. J. Power and R. H. Street) Flexible limits for 2-categories, J. Pure Appl. Algebra 61 (1989) 1–27.
  63. (with A. Carboni and R. J. Wood) A 2-categorical approach to change of base and geometric morphisms I, Cahiers de topologieet géométrie différentielle catégoriques 32 (1991) 47–95.
  64. A note on relations relative to a factorization system, Lecture Notes in Math. 1448 (Springer-Verlag, 1991) 249–261.
  65. On clubs and data-type constructors, in Applications of Categories to Computer Science (Proc. LMS Symposium, Durham 1991) (Cambridge Univ. Press 1992) 163–190.
  66. (with S. Lack) Finite-product-preserving functors, Kan extensions, and strongly-finitary 2-monads, Applied Categorical Structures 1 (1993) 85–94.
  67. (with S. Lack and R. F. C. Walters) Coinverters and categories of fractions for categories with structure, Applied Categorical Structures1 (1993) 95–102.
  68. (with A. J. Power) Adjunctions whose counits are coequalizers and presentations of finitary enriched monads, J. Pure Appl. Algebra 89 (1993) 163–179.
  69. (with A. Carboni and M. C. Pedicchio) Some remarks on Maltsev and Goursat categories, Applied Categorical Structures 1 (1993) 385–421.
  70. (with G. Janelidze) Galois theory and a general notion of central extension, J. Pure Appl. Algebra 97 (1994) 135–161.
  71. (with A. Carboni, G. Janelidze and R. Paré) On localization and stabilization for factorization systems, Applied Categorical Structures 5 (1997) 1–58.
  72. (with G. Janelidze) The reflectiveness of covering morphisms in algebra and geometry, Theory and Applications of Categories 3 (1997) 132–159.
  73. (with I. Le Creurer) On the monadicity over graphs of categories with limits, Cahiersde topologie et géométrie différentielle catégoriques38 (1997) 179–191.
  74. (with S. Lack) On property-like structures, Theory and Applications of Categories 3 (1997) 213–250.
  75. (with A. Carboni, D. Verity and R. J. Wood) A 2-categorical approach to change of base and geometric morphisms II, Theory and Applications of Categories 4 (1998) 82–136.
  76. (with S. Kasangian and V. Vighi) A bicategorical approach to information flow and security, in Categorical Studies in Italy, Rendiconti del Circolo Matematico di Palermo 64 (2000) 99–122.
  77. (with S. Lack) On the monadicity of categories with chosen colimits, Theory and Applications of Categories 7 (2000) 148–170.
  78. (with J. Adámek) M-completeness is seldom monadic over graphs, Theory and Applications of Categories 7 (2000) 171–205.
  79. (with G. Janelidze) Central extensions in Malt’sev varieties, Theory and Applications of Categories 7 (2000) 219–226.
  80. (with E. Faro) On the canonical algebraic structure of a category, J. Pure Appl. Algebra 154 (2000) 159–176.
  81. (with G. Janelidze) Central extensions in universal algebra: a unification of three notions, Algebra Universalis 44 (2000) 123–128.
  82. (with S. Lack) V-Cat is locally presentable or locally bounded when V is so, Theory and Applications of Categories 8 (2001) 555–575.
  83. (with G. Janelidze) A note on actions of a monoidal category, Theory and Applications of Categories 9 (2001) 61–91.
  84. (with A. Labella, R. Street and V. Schmitt) Categories enriched on both sides, J. Pure Appl. Algebra 168 (2002) 53–98.
  85. (with S. Lack) Monoidal functors generated by adjunctions, with applications to transport of structure along an equivalence, Fields Institute Communications 43 (2004) 319–340. Gregory Maxwell Kelly 1930–2007 251
  86. On the operads of J. P. May, Reprints in Theory and Applications of Categories 13 (2005) 1–13.
  87. (with V. Schmitt) Notes on enriched categories with colimits of some class, Theory and Applications of Categories 14 (2005) 399–423.
  88. (with F. Borceux and G. Janelidze) On the representability of actions in a semi-abelian category, Theory and Applications of Categories14 (2005) 244–286.
  89. (with F. Borceux and G. Janelidze) Internal object actions, Commentationes Mathematicae Universitatis Carolinae 46 (2005) 235–255.
  90. Basic concepts of enriched category theory, Reprint of the 1982 original [Cambridge Univ. Press, Cambridge], Reprints in Theory and Applications of Categories 10 (2005).
  91. The beginnings of category theory in Australia, in “Categories in algebra, geometry and mathematical physics”, Contemporary Math. 431 (Amer. Math. Soc. , Providence, RI, 2007) 1–6.
  92. (with A. Carboni, R. F. C. Walters and R. J. Wood) Cartesian bicategories II, Theory and Applications of Categories 19 (2008) 93–124.
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