Commutativity

By R. Garner, Ignacio L'opez Franco. 2015

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We describe a general framework for notions of commutativity based on enriched category theory. We extend Eilenberg and Kelly's tensor product for categories enriched over a symmetric monoidal base to a tensor product for categories enriched over a normal duoidal category; using this, we re-find notions such as the commutativity of a finitary algebraic theory or a strong monad, the commuting tensor product of two theories, and the Boardman-Vogt tensor product of symmetric operads.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d16e3a6be59b951eb26f9a74e68700e933792733