An embedding theorem for adhesive categories

Stephen Lack*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)


    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.

    Original languageEnglish
    Pages (from-to)180-188
    Number of pages9
    JournalTheory and Applications of Categories
    Publication statusPublished - 2011


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