Coherence for Skew-Monoidal Categories

Tarmo Uustalu

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.

In Paul Levy and Neel Krishnaswami: Proceedings 5th Workshop on Mathematically Structured Functional Programming (MSFP 2014), Grenoble, France, 12 April 2014, Electronic Proceedings in Theoretical Computer Science 153, pp. 68–77.
Published: 5th June 2014.

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