2024/03/26 by Redi Haderi, Haderi, Redi, Cihan Okay +3
Mathematics · Computer Science · #Advanced Banach Space Theory #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2403.18102
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 \scrO-monoidal categories, we state and prove a Grothendieck construction for lax \scrO-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.