Issue Theoret. Informatics Appl. Volume 39, Number 3, July-September 2005 Foundations of Software Science and Computer Structures (FOSSACS'04) Page(s) 511 - 545 DOI 10.1051/ita:2005028

Theoret. Informatics Appl. 39, 511-545 (2005)
DOI: 10.1051/ita:2005028

Adhesive and quasiadhesive categories

Stephen Lack¹ and Pawel Sobocinski<sup>2

1</sup>  School of Quantitative Methods and Mathematical Sciences, University of Western Sydney, Australia.
²  BRICS, University of Aarhus, Denmark; pawel@brics.dk

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.

Mathematics Subject Classification. 18A30, 18A35, 18D99, 68Q42, 68Q65

Key words: Adhesive categories -- quasiadhesive categories -- extensive categories -- category theory -- graph rewriting


© EDP Sciences 2005

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