On the axioms for adhesive and quasiadhesive categories

Details On the axioms for adhesive and quasiadhesive categories On the axioms for adhesive and quasiadhesive categories

2011-08-15

arxiv.org/abs/1108.2934v1

Mathematics

Category Theory

21 pages

Scientific paper

A category is adhesive if it has all pullbacks, all pushouts along monomorphisms, and all exactness conditions between pullbacks and pushouts along monomorphisms which hold in a topos. This condition can be modified by considering only pushouts along regular monomorphisms, or by asking only for the exactness conditions which hold in a quasitopos. We prove four characterization theorems dealing with adhesive categories and their variants.

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