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.