Bulletin of the American Mathematical Society

MathSciNet review: 1567445
Full text of review: PDF   This review is available free of charge.
Book Information:

Author: G. M. Kelly
Title: Basic concepts of enriched category theory
Additional book information: London Mathematical Society Lecture Note Series, No. 64, Cambridge Univ. Press, New York, 1982, 245 pp., $24.95. ISBN 0-5212-8702-2.

F. F. Bonsall, A down-to-earth view of mathematics, Amer. Math. Monthly 89 (1982), no. 1, 8–15. MR 639769, DOI 10.2307/2320989

B. J. Day and G. M. Kelly, Enriched functor categories, Reports of the Midwest Category Seminar, III, Springer, Berlin, 1969, pp. 178–191. MR 0255633

Eduardo J. Dubuc, Kan extensions in enriched category theory, Lecture Notes in Mathematics, Vol. 145, Springer-Verlag, Berlin-New York, 1970. MR 0280560

4.

C. Ehresmann, Oeuvres complètes et commentees, Partie III, Cahiers Topologie et Géom. Différentielle 21 (1980), Supplément 1 et 2.

Samuel Eilenberg and G. Max Kelly, Closed categories, Proc. Conf. Categorical Algebra (La Jolla, Calif., 1965) Springer, New York, 1966, pp. 421–562. MR 0225841

Peter Gabriel and Friedrich Ulmer, Lokal präsentierbare Kategorien, Lecture Notes in Mathematics, Vol. 221, Springer-Verlag, Berlin-New York, 1971 (German). MR 0327863

Robert I. Goldblatt, Topoi, Studies in Logic and the Foundations of Mathematics, vol. 98, North-Holland Publishing Co., Amsterdam-New York, 1979. The categorical analysis of logic. MR 551362

John W. Gray, The categorical comprehension scheme, Category Theory, Homology Theory and their Applications, III (Battelle Institute Conference, Seattle, Wash., 1968, Vol. Three), Springer, Berlin, 1969, pp. 242–312. MR 0249483

John W. Gray, Formal category theory: adjointness for $2$-categories, Lecture Notes in Mathematics, Vol. 391, Springer-Verlag, Berlin-New York, 1974. MR 0371990

John W. Gray, Fragments of the history of sheaf theory, Applications of sheaves (Proc. Res. Sympos. Appl. Sheaf Theory to Logic, Algebra and Anal., Univ. Durham, Durham, 1977) Lecture Notes in Math., vol. 753, Springer, Berlin, 1979, pp. 1–79. MR 555539

P. T. Johnstone, Topos theory, London Mathematical Society Monographs, Vol. 10, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1977. MR 0470019

G. M. Kelly, Adjunction for enriched categories, Reports of the Midwest Category Seminar, III, Springer, Berlin, 1969, pp. 166–177. MR 0255632

G. M. Kelly, Structures defined by finite limits in the enriched context. I, Cahiers Topologie Géom. Différentielle 23 (1982), no. 1, 3–42. Third Colloquium on Categories, Part VI (Amiens, 1980). MR 648793

G. M. Kelly and Ross Street, Review of the elements of $2$-categories, Category Seminar (Proc. Sem., Sydney, 1972/1973) Lecture Notes in Math., Vol. 420, Springer, Berlin, 1974, pp. 75–103. MR 0357542

Anders Kock, Synthetic differential geometry, London Mathematical Society Lecture Note Series, vol. 51, Cambridge University Press, Cambridge-New York, 1981. MR 649622

F. William Lawvere, An elementary theory of the category of sets, Proc. Nat. Acad. Sci. U.S.A. 52 (1964), 1506–1511. MR 172807, DOI 10.1073/pnas.52.6.1506

F. William Lawvere, The category of categories as a foundation for mathematics, Proc. Conf. Categorical Algebra (La Jolla, Calif., 1965) Springer, New York, 1966, pp. 1–20. MR 0207517

F. E. J. Linton, Autonomous categories and duality of functors, J. Algebra 2 (1965), 315–349. MR 180587, DOI 10.1016/0021-8693(65)90013-X

Saunders Mac Lane, Categories for the working mathematician, 2nd ed., Graduate Texts in Mathematics, vol. 5, Springer-Verlag, New York, 1998. MR 1712872

Michael Makkai and Gonzalo E. Reyes, First order categorical logic, Lecture Notes in Mathematics, Vol. 611, Springer-Verlag, Berlin-New York, 1977. Model-theoretical methods in the theory of topoi and related categories. MR 0505486

Ernest G. Manes, Algebraic theories, Graduate Texts in Mathematics, No. 26, Springer-Verlag, New York-Heidelberg, 1976. MR 0419557

L. D. Nel, Enriched algebraic categories with applications in functional analysis, Categorical aspects of topology and analysis (Ottawa, Ont., 1980) Lecture Notes in Math., vol. 915, Springer, Berlin-New York, 1982, pp. 247–259. MR 659896

Joan Wick Pelletier, KAN extensions of the HOM functor in the category of Banach spaces, Ann. Sci. Math. Québec 4 (1980), no. 1, 59–71 (English, with French summary). MR 574834

Ross Street, Fibrations in bicategories, Cahiers Topologie Géom. Différentielle 21 (1980), no. 2, 111–160. MR 574662

Ross Street, Conspectus of variable categories, J. Pure Appl. Algebra 21 (1981), no. 3, 307–338. MR 617138, DOI 10.1016/0022-4049(81)90021-9

26.

J.-L. Verdier, Topologies et faiscaux S. G. A. A. fasc. I., 1963-64.

1.

F. F. Bonsall, A down-to-earth view of mathematics, Amer. Math. Monthly 89 (1982), 8-15. MR 0639769

2.

B. J. Day and G. M. Kelly, Enriched functor categories, Lecture Notes in Math., vol. 106, Springer-Verlag, Berlin and New York, 1969, pp. 179-191. MR 255633

3.

E. J. Dubuc, Kan extensions in enriched category theory, Lecture Notes in Math., vol. 145, Springer-Verlag, Berlin and New York, 1970. MR 280560

4.

C. Ehresmann, Oeuvres complètes et commentees, Partie III, Cahiers Topologie et Géom. Différentielle 21 (1980), Supplément 1 et 2.

5.

S. Eilenberg and G. M. Kelly, Closed categories, Proc. Conf. Categorical Algebra (La Jolla, 1965), Springer-Verlag, New York, 1966, pp. 421-562. MR 225841

6.

P. Gabriel and F. Ulmer, Lokal Präsentierbare Kategorien, Lecture Notes in Math., vol. 221, Springer-Verlag, Berlin and New York, 1971. MR 327863

7.

R. Goldblatt, Topoi, the categorical analysis of logic, North-Holland, Amsterdam, 1979. MR 551362

8.

J. W. Gray, The categorical comprehension scheme, Lecture Notes in Math., vol. 99, Springer-Verlag, Berlin and New York, 1969, pp. 242-312. MR 249483

9.

J. W. Gray, Formal category theory: Adjointness for 2-categories, Lecture Notes in Math., vol. 391, Springer-Verlag, Berlin and New York, 1974. MR 371990

10.

J. W. Gray, Fragments of the history of sheaf theory, Lecture Notes in Math., vol 753, Springer-Verlag, Berlin and New York, 1979, pp. 1-79. MR 555539

11.

P. Johnstone, Topos theory, London Math. Soc. Monographs, no. 10, Academic Press, New York, 1977. MR 470019

12.

G. M. Kelly, Adjunction for enriched categories, Lecture Notes in Math., vol. 106, Springer-Verlag, Berlin and New York, 1969, pp. 166-177. MR 255632

13.

G. M. Kelly, Structures defined by finite limits in the enriched context. I, Cahiers Topologie Géom. Différentielle 23 (1982), 3-42. MR 648793

14.

G. M. Kelly and R. H. Street, Review of the elements of 2-categories, Lecture Notes in Math., vol. 420, Springer-Verlag, Berlin and New York, 1974, pp. 75-103. MR 357542

15.

A. Kock, Synthetic differential geometry, London Math. Soc. Lecture Note Ser., No. 51, Cambridge Univ. Press, New York, 1981. MR 649622

16.

F. W. Lawvere, An elementary theory of the category of sets, Proc. Nat. Acad. Sci. U.S.A. 52 (1964), 1506-1511. MR 172807

17.

F. W. Lawvere, The category of categories as a foundation for mathematics, Proc. Conf. Categorical Algebra (La Jolla, 1965), Srpinger-Verlag, New York, 1966, pp. 1-20. MR 207517

18.

F. E. J. Linton, Autonomous categories and duality of functors, J. Algebra 2 (1965), 315-349. MR 180587

19.

S. Mac Lane, Categories for the working mathematician, Springer-Verlag, New York, 1971. MR 1712872

20.

M. Makkai and G. E. Reyes, First order categorical logic, Lecture Notes in Math., vol. 611, Springer-Verlag, Berlin and New York, 1977. MR 505486

21.

E. G. Manes, Algebraic theories, Springer-Verlag, New York, 1976. MR 419557

22.

L. D. Nel, Enriched algebraic categories with applications in functional analysis, Lecture Notes in Math., vol. 915, Springer-Verlag, Berlin and New York, 1982, pp. 247-259. MR 659896

23.

J. W. Pelletier, Kan extensions of the hom functor in the category of Banach spaces, Ann. Sci. Math. Québec 4 (1980), 59-71. MR 574834

24.

R. H. Street, Fibrations in bicategories, Cahiers Topologie Géom. Différentielle 21 (1980), 111-160. MR 574662

25.

R. H. Street, Conspectus of variable categories, J. Pure. Appl. Algebra 21 (1981), 307-338. MR 617138

26.

J.-L. Verdier, Topologies et faiscaux S. G. A. A. fasc. I., 1963-64.