302 citations · 2.7k across the 73 of their papers we have counts for
6 papers · 1 filter
Dilations and information flow axioms in categorical probability
Tobias Fritz, Tomáš Gonda, Nicholas Gauguin Houghton-Larsen +3
We study the positivity and causality axioms for Markov categories as properties of dilations and information flow in Markov categories, and in variations thereof for arbitrary sem…
The d-separation criterion in Categorical Probability
Tobias Fritz, Andreas Klingler
The d-separation criterion detects the compatibility of a joint probability distribution with a directed acyclic graph through certain conditional independences. In this work, we s…
Non-abelian and -curved homological algebra with arrow categories
Tobias Fritz
Grandis's non-abelian homological algebra generalizes standard homological algebra in abelian categories to \textit{homological categories}, which are a broader class of categories…
Asymptotic and catalytic containment of representations of
Tobias Fritz
Given two finite-dimensional representations and of , when is there such that is isomorphic to a subrepresentation of $σ^…
From Gs-monoidal to Oplax Cartesian Categories: Constructions and Functorial Completeness
Tobias Fritz, Fabio Gadducci, Davide Trotta +1
Originally introduced in the context of the algebraic approach to term graph rewriting, the notion of gs-monoidal category has surfaced a few times under different monikers in the…
Free gs-monoidal categories and free Markov categories
Tobias Fritz, Wendong Liang
Categorical probability has recently seen significant advances through the formalism of Markov categories, within which several classical theorems have been proven in entirely abst…