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The operadic theory of convexity
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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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Cited by 1 Pith paper
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The geometry of simplicial distributions on suspension scenarios
For a connected measurement space X, the non-signaling polytope of the cone scenario is the join of m copies of the original polytope, and the suspension scenario is characterized by a pullback of two such joins.
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