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Upcoming paper: Rewriting for monoidal closed categories at FSCD 2022

Rewriting for monoidal closed categories

David SprungerDan GhicaFabio Zanasi and Mario Alvarez-Picallo. 

This paper develops a formal string diagram language for monoidal closed categories. Previous work
has shown that string diagrams for freely generated symmetric monoidal categories can be viewed
as hypergraphs with interfaces, and the axioms of these categories can be realized by rewriting
systems. This work proposes hierarchical hypergraphs as a suitable formalization of string diagrams
for monoidal closed categories. We then show double pushout rewriting captures the axioms of these
closed categories.
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