Comments:

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

Abstract:

Basic Concepts of Enriched Category Theory by G.M. Kelly Originally published as: Cambridge University Press, Lecture Notes in Mathematics 64, 1982. TAC Reprints Home Received by the editors 10--30--2004. Transmitted by Steve Lack, Ross Street and RJ Wood. Reprint published on 04--23-2005. 2000 Mathematics Subject Classification: 18--02, 18D10, 18D20. Key words and phrases: enriched categories, monoidal categories. London Mathematical Society Lecture Notes Series 64, 1982. vi CONTENTS Introduction 1 1 The elementary notions7 1.1 Monoidal categories 7 1.2 The 2category V, CAT for a monoidalV Bibliography125 Index131 2. Functor categories 27 2.1 Ends in V 27 3.12 The existence of a limit, and colimit, preserving universe enlargement V to enlarged V56 4 Kan extensions59 4.1 The definition of Kan extensions; their expressibility by limits and colimits 59 4.2 Elementary properties and examples 61 4.3 A universal property of LanKG; its inadequacy as a definition 64 4.4 Iterated Kan extensions; Kan adjoints; (Aop, V)as the free cocompletion 66 4.5 Initial diagrams as the left Kan extensions into V 68 4.6 Filtered categories when V is Set 71 4.7 Factorization into an initial functor and a discrete opfibration 73 4.8 The general representability and adjoint functor theorems 75 4.9 Representability and adjoint functor theorems when V is Set 77 4.10 Existence and characterization of the left Kan extension 80 5 Density 85 Republished in: Reprints in Theory and Applications of Categories, No. 10 (2005) pp. 1--136 Keywords: enriched categories, monoidal categories 2000 MSC: 18D10, 18D20.

Rights:

Originally published as: Cambridge University Press, Lecture Notes in Mathematics 64, 1982. Republished in: Reprints in Theory and Applications of Categories, No. 10 (2005) pp. 1--136 http://www.tac.mta.ca/tac/reprints/articles/10/tr10.dvi http://www.tac.mta.ca/tac/reprints/articles/10/tr10.ps Copyright by G.M. Kelly, 2005. Permission to copy for private use granted. http://www.tac.mta.ca/tac/reprints/articles/10/tr10.pdf TAC Reprints Home

No messages.