References on information cohomology#

Some references on the cohomological nature of various information theoretic concepts such as entropy and relative information.

Markov categories#

Markov categories were defined by Fritz [Fri20].

Perrone on Markov categories and entropy [Per22].

Kochen reconstructs quantum mechanics using sigma complexes [Koc15].

Homological nature of entropy by Baudot and Bennequin [BB15].

Generalized information structures by Vigneaux [Vig17]. Vigneaux’s PhD thesis can be found here.

Bradley describes entropy as a topological operad derivation [Bra21].

Manin and Marcolli explores homotopy-theoretic and categorical models of neural information networks [MM20].

BB15: Pierre Baudot and Daniel Bennequin. The homological nature of entropy. Entropy, 17(5):3253–3318, 2015.
Bra21: Tai-Danae Bradley. Entropy as a topological operad derivation. Entropy, 23(9):1195, 2021.
Fri20: Tobias Fritz. A synthetic approach to markov kernels, conditional independence and theorems on sufficient statistics. Advances in Mathematics, 370:107239, 2020.
Koc15: Simon Kochen. A reconstruction of quantum mechanics. Foundations of Physics, 45:557–590, 2015.
MM20: Yuri Manin and Matilde Marcolli. Homotopy theoretic and categorical models of neural information networks. arXiv preprint arXiv:2006.15136, 2020.
Per22: Paolo Perrone. Markov categories and entropy. arXiv preprint arXiv:2212.11719, 2022.
Vig17: Juan Pablo Vigneaux. Information structures and their cohomology. arXiv preprint arXiv:1709.07807, 2017.