Cofibrations in the bicategory of topoi
type: Item
instance of: scholarly article
title: Cofibrations in the bicategory of topoi
zbMATH Open document ID: 0535.18006
DOI: 10.1016/0022-4049(84)90016-1
published in: Journal of Pure and Applied Algebra
publication date: 1984-01-01T00:00:00Z
review text: Within a bicategory H it is possible to define which spans are cofibrations and which are codiscrete. If H admits certain universal constructions and these are well-behaved then codiscrete cofibrations between objects of H become the arrows of a bicategory M. When H is the bicategory of hom-enriched categories over a given base where the arrows of H are enriched functors, codiscrete cofibrations amount to modules (profunctors), and cofibrations amount to ''gamuts''; that is, normal morphisms of bicategories from the ordered set 3 into M [the reviewer, Cah. Topologie Géom. Différ. 21, 111-159 (1980; Zbl 0436.18005)]. The present paper starts with the bicategory H of topoi and geometric morphisms and shows that codiscrete cofibrations in H are left-exact functors between topoi. Also it is shown that cofibrations in this H are gamuts in the resultant M.
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 18B25
Mathematics Subject Classification ID: 18D20
zbMATH DE Number: 3849459
zbMATH Keywords: proarrows
zbMATH Keywords: bicategory
zbMATH Keywords: cofibrations
zbMATH Keywords: codiscrete
zbMATH Keywords: gamuts
zbMATH Keywords: topoi
zbMATH Keywords: left- exact functors
author: Robert Rosebrugh
author: R. J. Wood
reviewed by: Ross H. Street
MaRDI profile type: Publication
full work available at URL: 0022-4049(84)90016-1
OpenAlex ID: W2041754115
cites work: Atomic toposes
cites work: Q5586462
cites work: Q4145861
cites work: Open maps of toposes
cites work: Q4170869
cites work: Q3876103
cites work: Yoneda structures on 2-categories
cites work: Q3961635
cites work: Artin glueing
description: scientific article; zbMATH DE number 3849459