Information and Computation
Abstract and concrete categories
Abstract and concrete categories
Basic category theory for computer scientists
Basic category theory for computer scientists
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
Adhesive High-Level Replacement Systems: A New Categorical Framework for Graph Transformation
Fundamenta Informaticae - SPECIAL ISSUE ON ICGT 2004
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
Van Kampen colimits as bicolimits in span
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
Adhesivity is not enough: local church-rosser revisited
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Adhesivity with Partial Maps instead of Spans
Fundamenta Informaticae - Recent Developments in the Theory of Graph Transformation, 2010
Refined graph rewriting in span-categories: a framework for algebraic graph transformation
ICGT'12 Proceedings of the 6th international conference on Graph Transformations
M,N-adhesive transformation systems
ICGT'12 Proceedings of the 6th international conference on Graph Transformations
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The introduction of adhesive categories revived interest in the study of properties of pushouts with respect to pullbacks, which started over thirty years ago in the category of graphs. Adhesive categories provide a single property of pushouts that suffices to derive lemmas that are essential for central theorems of double pushout rewriting such as the local Church-Rosser Theorem. The present paper shows that the same lemmas already hold for pushouts that are hereditary, i.e. those pushouts that remain pushouts when they are embedded into the associated category of partial maps. Hereditary pushouts - a twenty year old concept - induce a generalization of adhesive categories, which will be dubbed partial map adhesive. An application relevant category that does not fit the framework of adhesive categories and its variations in the literature will serve as an illustrating example of a partial map adhesive category.