Kan Extensions in Enriched Category Theory

DUBUC, EDUARDO J.

Springer Verlag Berlin

Lugar: Heidelberg, Alemania; Año: 1970 p. 189

<!-- @page { size: 8.5in 11in; margin: 0.79in } P { margin-bottom: 0.08in } -->                    PREFACE Category Theory is rapidly coming of age as a Mathematical discipline. In this process it now ap- pears that a central rolle will be played by the notion of an enriched category. These categories, with hom-sets in a closed category,--in particular, in a symmetric monoidal closed categorie-- semeed initially very complez and difficult to manage effectively. However, independent work by various experts—Yoneda, Linton, Benabou, Eilenberg-Kelly, Lambek, Bunge, Ulmer, Gray, Palmquist, and others-- step was the discovery of the proper use of tensors, cotensors, and Kan extensions for enriched categories (A discovery made simultaneously and independently by Benabou and by Kelly with Day). As a result, an efficient presentation of enriched categories is now possible. This paper by Dubuc collects all these ideas in a compact exposition wich makes this efficiency very clear—and wich also serve as a basis for Dubuc's own original contributions. I have, there- fore, recommended to the editors of the Lecture Notes series the rapid publication of this paper, to pro- vide easy acces to this foundation for future devel-opment.                                       Saunders Mac Lane