The operadic theory of convexity
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916179528908800 |
|---|---|
| author | Haderi, Redi Okay, Cihan Stern, Walker H. |
| author_facet | Haderi, Redi Okay, Cihan Stern, Walker H. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18102 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The operadic theory of convexity Haderi, Redi Okay, Cihan Stern, Walker H. Category Theory Information Theory Quantum Physics 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. |
| title | The operadic theory of convexity |
| topic | Category Theory Information Theory Quantum Physics |
| url | https://arxiv.org/abs/2403.18102 |