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Book Information

Author(s): 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

1.: F. F. Bonsall, A down-to-earth view of mathematics, Amer. Math. Monthly 89 (1982), 8-15. MR 639769
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.

Review Information:
Journal: Bull. Amer. Math. Soc. 9 (1983), 102-107.
DOI: 10.1090/S0273-0979-1983-15172-8
PII: S 0273-0979(1983)15172-8

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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