An embedding theorem for adhesive categories

Details An embedding theorem for adhesive categories An embedding theorem for adhesive categories

2011-03-03

arxiv.org/abs/1103.0600v1

Theory and Applications of Categories, Vol. 25, No. 7, 2011, pp. 180-188

Mathematics

Category Theory

8 pages

Scientific paper

Adhesive categories are categories which have pushouts with one leg a monomorphism, all pullbacks, and certain exactness conditions relating these pushouts and pullbacks. We give a new proof of the fact that every topos is adhesive. We also prove a converse: every small adhesive category has a fully faithful functor in a topos, with the functor preserving the all the structure. Combining these two results, we see that the exactness conditions in the definition of adhesive category are exactly the relationship between pushouts along monomorphisms and pullbacks which hold in any topos.

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