On completeness of locally-internal categories
type: Item
instance of: scholarly article
title: On completeness of locally-internal categories
zbMATH Open document ID: 0631.18005
DOI: 10.1016/0022-4049(87)90055-7
published in: Journal of Pure and Applied Algebra
publication date: 1987-01-01T00:00:00Z
review text: This paper will certainly be considered as a very interesting one by those people who believe that the theory of enriched categories is an elegant tool for explaining things in mathematics... but it will probably not be appreciated by some of those people who consider fibered categories as a more intuitive notion. In any case I did appreciate this paper very much. The basic idea is to view a category which is fibered over SETS as a category enriched in the bicategory of spans of sets. For enriched categories, there is an obvious extension of the classical notions of limit or completeness: when the fibered category is viewed as indicated, this gives precisely the apparently more sophisticated notion of completeness for fibrations. All those results are in fact proved in a much more general context, where SETS is replaced by an arbitrary topos.
reviewed by: F. Borceux
Mathematics Subject Classification ID: 18D20
Mathematics Subject Classification ID: 18B25
Mathematics Subject Classification ID: 18A35
Mathematics Subject Classification ID: 18D30
Mathematics Subject Classification ID: 18D05
zbMATH DE Number: 4025659
zbMATH Keywords: enriched categories
zbMATH Keywords: fibered categories
zbMATH Keywords: bicategory of spans
zbMATH Keywords: limit
zbMATH Keywords: completeness
zbMATH Keywords: topos
author: Renato Betti
author: R. F. C. Walters
MaRDI profile type: Publication
full work available at URL: 0022-4049(87)90055-7
OpenAlex ID: W1997429906
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description: scientific article; zbMATH DE number 4025659