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We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are well-behaved, as well as quasiadhesive categories which restrict attention to regular monomorphisms. Many examples of graphical structures used in computer science are shown to be examples of adhesive and quasiadhesive categories. Double-pushout graph rewriting generalizes well to rewriting on arbitrary adhesive and quasiadhesive categories.
We introduce adhesive categories, which are
categories with structure ensuring that pushouts along monomorphisms
are well-behaved, as well as quasiadhesive categories which
restrict attention to regular monomorphisms.
Many examples of graphical structures used in computer
science are shown to be examples of adhesive and quasiadhesive
categories. Double-pushout graph rewriting generalizes well to
rewriting on arbitrary adhesive and quasiadhesive categories.
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