Information and Computation
Abstract and concrete categories
Abstract and concrete categories
Basic category theory for computer scientists
Basic category theory for computer scientists
Algebraic approach to single-pushout graph transformation
Theoretical Computer Science - Special issue on selected papers of the International Workshop on Computing by Graph Transformation, Bordeaux, France, March 21–23, 1991
Handbook of graph grammars and computing by graph transformation
Graph Rewriting in Some Categories of Partial Morphisms
Proceedings of the 4th International Workshop on Graph-Grammars and Their Application to Computer Science
Double-pushout graph transformation revisited
Mathematical Structures in Computer Science
Graph-grammars: An algebraic approach
SWAT '73 Proceedings of the 14th Annual Symposium on Switching and Automata Theory (swat 1973)
Quasitoposes, quasiadhesive categories and artin glueing
CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
Hereditary pushouts reconsidered
ICGT'10 Proceedings of the 5th international conference on Graph transformations
Adhesive High-Level Replacement Systems: A New Categorical Framework for Graph Transformation
Fundamenta Informaticae - SPECIAL ISSUE ON ICGT 2004
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The introduction of adhesive categories revived interest in the study of properties of pushouts with respect to pullbacks that started over thirty years ago for the category of graphs. Adhesive categories - of which graphs are the “archetypal” example - are defined by a single property of pushouts along monos that implies essential lemmas and central theorems of double pushout rewriting such as the local Church-Rosser Theorem. The present paper shows that a strictly weaker condition on pushouts suffices to obtain essentially the same results: it suffices to require pushouts to be hereditary, i.e. they have to remain pushouts when they are embedded into the associated category of partial maps. This fact however is not the only reason to introduce partial map adhesive categories as categories with pushouts along monos (of a certain stable class) that are hereditary. There are two equally important motivations: first, there is an application relevant example category that cannot be captured by the more established variations of adhesive categories; second, partial map adhesive categories are “conceptually similar” to adhesive categories as the latter can be characterized as those categories with pushout along monos that remain bi-pushouts when they are embedded into the associated bi-category of spans. Thus, adhesivity with partial maps instead of spans appears to be a natural candidate for a general rewriting framework.