Adhesive and quasiadhesive categories
School of Quantitative Methods
and Mathematical Sciences, University of Western Sydney, Australia.
2 BRICS, University of Aarhus, Denmark; email@example.com
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.
Mathematics Subject Classification: 18A30 / 18A35 / 18D99 / 68Q42 / 68Q65
Key words: Adhesive categories / quasiadhesive categories / extensive categories / category theory / graph rewriting
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