# A category theoretical approach to the concurrent semantics of rewriting: adhesive categories and related concepts

@inproceedings{Heindel2009ACT, title={A category theoretical approach to the concurrent semantics of rewriting: adhesive categories and related concepts}, author={Tobias Heindel}, year={2009} }

This thesis studies formal semantics for a family of rewriting formalisms that have arisen as category theoretical abstractions of the so-called algebraic approaches to graph rewriting. The latter in turn generalize and combine features of term rewriting and Petri nets. Two salient features of (the abstract versions of) graph rewriting are a suitable class of categories which captures the structure of the objects of rewriting, and a notion of independence or concurrency of rewriting steps – as… Expand

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#### 20 Citations

Processes and unfoldings: concurrent computations in adhesive categories

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Adhesivity with Partial Maps instead of Spans

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Adhesivity with partial maps instead of spans appears to be a natural candidate for a general rewriting framework 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. Expand

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An algebraic approach to stochastic graph-rewriting which extends the classical construction of the Heisenberg-Weyl algebra and its canonical representation on the Fock space and finds that natural variants of the evaluation morphism map give rise to concepts of graph transformations hitherto not considered. Expand

Single Pushout Rewriting in Comprehensive Systems

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