Cofibrations in the bicategory of topoi
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.
scientific article; zbMATH DE number 3849459