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. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Johnstone, P. T., Lack, S., & Sobociński, P. (2007). Quasitoposes, quasiadhesive categories and artin glueing. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4624 LNCS, pp. 312–326). Springer Verlag. https://doi.org/10.1007/978-3-540-73859-6_21
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