# Free skew monoidal categories

@article{Bourke2017FreeSM,
title={Free skew monoidal categories},
author={John Bourke and Stephen Lack},
journal={Journal of Pure and Applied Algebra},
year={2017}
}
• Published 21 August 2017
• Mathematics
• Journal of Pure and Applied Algebra
• Mathematics
ACT
• 2020
This paper develops sequent calculi for partially normal skew monoidal categories, which are skew monoid categories with one or more structural laws invertible, and proves cut elimination and shows that the calculi admit focusing.
It is well-known that the "pre-2-category" $\mathscr{C}at_\mathrm{dg}^\mathrm{coh}(k)$ of small dg categories over a field $k$, with 1-morphisms defined as dg functors, and with 2-morphisms defined
The goal of this thesis is to devise a principled semantic framework for verifying programs with arbitrary monadic effects in a generic way with respect to rich specifications, for properties such as program equivalence.
• Mathematics
• 2018
Szlach´anyi’s skew monoidal categories are a well-motivated variation of monoidal categories in which the unitors and associator are not required to be natural isomorphisms, but merely natural

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A variation of monoidal categories called skew-monoidal cat- egories where the unital and associativity laws are not required to be isomorphisms, only natural transformations is motivated, and a proof of this coherence proof is presented.
Author's Note. When this manuscript was submitted in January 1972, the editor asked that it be expanded to study the relation of operads to clubs. The author found this too daunting a task at a busy
We study Quillen model categories equipped with a monoidal skew closed structure that descends to a genuine monoidal closed structure on the homotopy category. Our examples are 2-categorical and