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arXiv · 1406.2064

Coherence for Skew-Monoidal Categories

Tarmo Uustalu
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Abstract

I motivate a variation (due to K. Szlachányi) of monoidal categories called skew-monoidal categories where the unital and associativity laws are not required to be isomorphisms, only natural transformations. Coherence has to be formulated differently than in the well-known monoidal case. In my (to my knowledge new) version, it becomes a statement of uniqueness of normalizing rewrites. I present a proof of this coherence theorem and also formalize it fully in the dependently typed programming language Agda.

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Tarmo Uustalu. 2014-06-09. Coherence for Skew-Monoidal Categories. https://doi.org/10.4204/eptcs.153.5

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