On the axioms for adhesive and quasiadhesive categories

Richard Garner and Stephen Lack

A category is adhesive if it has all pullbacks, all push-outs 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.

Keywords: adhesive category, quasiadhesive category, pushout, exactness condition, embedding theorem

2010 MSC: 18A30, 18B15

Theory and Applications of Categories, Vol. 27, 2012, No. 3, pp 27-46.

Published 2012-05-07.


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