Quasitoposes, Quasiadhesive Categories and Artin Glueing

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.

• Type: Conference
• Year: 2007
• Where: CALCO
• Authors: Peter T. Johnstone, Stephen Lack, Pawel Sobocinski
• Keywords: Adhesive Categories, CALCO 2007, Many Examples, Quasiadhesive Categories