Geodesic
An embedding theorem for adhesive categories
Theory and applications of categories, Tome 25 (2011), pp. 180-188 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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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Classification : 18A30, 18B15, 18B25
Keywords: adhesive category, topos, embedding theorem 
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     author = {Stephen Lack},
     title = {An embedding theorem for adhesive categories},
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     pages = {180--188},
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     volume = {25},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2011_25_a6/}
}
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Stephen Lack. An embedding theorem for adhesive categories. Theory and applications of categories, Tome 25 (2011), pp. 180-188. http://geodesic.mathdoc.fr/item/TAC_2011_25_a6/