Coherence for Skew-Monoidal Categories
Logic in Computer Science
2014-08-26 v1 Programming Languages
Category Theory
Abstract
I motivate a variation (due to K. Szlach\'{a}nyi) 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.
Keywords
Cite
@article{arxiv.1406.2064,
title = {Coherence for Skew-Monoidal Categories},
author = {Tarmo Uustalu},
journal= {arXiv preprint arXiv:1406.2064},
year = {2014}
}
Comments
In Proceedings MSFP 2014, arXiv:1406.1534