Quasitoposes, quasiadhesive categories and artin glueing

Authors:
Peter T. Johnstone;Stephen Lack;Paweł Sobociński
Affiliations:
DPMMS, University of Cambridge, United Kingdom;School of Computing and Mathematics, University of Western Sydney, Australia;ECS, University of Southampton, United Kingdom
Venue:
CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
Year:
2007

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Abstract

Adhesive categories are a class of categories in which pushouts along monos are well-behaved with respect to pullbacks. Recently it has been shown that any topos is adhesive. Many examples of interest to computer scientists are not adhesive, a fact which motivated the introduction of quasiadhesive categories. We show that several of these examples arise via a glueing construction which yields quasitoposes. We show that, surprisingly, not all such quasitoposes are quasiadhesive and characterise precisely those which are by giving a succinct necessary and sufficient condition on the lattice of subobjects.