Related papers: The operadic theory of convexity

The operadic theory of convexity

URL: http://arxiv.org/abs/2403.18102v1
Date: Tue, 26 Mar 2024 21:01:39 GMT
Title: The operadic theory of convexity
Authors: Redi Haderi, Cihan Okay, Walker H. Stern,
Abstract summary: We characterize convexity in terms of algebras over a PROP, and establish a tensor-product-like symmetric monoidal structure on the category of convex sets. We apply this construction to the categorical characterization of entropy of Baez, Fritz, and Leinster, and to the study of quantum contextuality in the framework of simplicial distributions.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: In this article, we characterize convexity in terms of algebras over a PROP, and establish a tensor-product-like symmetric monoidal structure on the category of convex sets. Using these two structures, and the theory of $\scr{O}$-monoidal categories, we state and prove a Grothendieck construction for lax $\scr{O}$-monoidal functors into convex sets. We apply this construction to the categorical characterization of entropy of Baez, Fritz, and Leinster, and to the study of quantum contextuality in the framework of simplicial distributions.

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