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Adhesive and quasiadhesive categories

Published online by Cambridge University Press:  15 July 2005

Stephen Lack  and
Paweł Sobociński
Stephen Lack
Affiliation:
School of Quantitative Methods and Mathematical Sciences, University of Western Sydney, Australia.
Paweł Sobociński
Affiliation:
BRICS, University of Aarhus, Denmark; pawel@brics.dk
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Abstract

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.

Keywords

Adhesive categoriesquasiadhesive categoriesextensive categoriescategory theorygraph rewriting

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