302 citations · 2.7k across the 73 of their papers we have counts for
13 papers · 1 filter
Nonunital Operator Systems as Modules in Enriched Category Theory
Tim Netzer, Tobias Fritz
An operator system is similar to a module over a ring, with the role of scalar multiplication played by the action of completely positive maps. Using enriched category theory, we m…
Weakly Markov categories and weakly affine monads
Tobias Fritz, Fabio Gadducci, Paolo Perrone +1
Introduced in the 1990s in the context of the algebraic approach to graph rewriting, gs-monoidal categories are symmetric monoidal categories where each object is equipped with the…
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…
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…
Weak cartesian properties of simplicial sets
Carmen Constantin, Tobias Fritz, Paolo Perrone +1
Many special classes of simplicial sets, such as the nerves of categories or groupoids, the 2-Segal sets of Dyckerhoff and Kapranov, and the (discrete) decomposition spaces of Gálv…
Partial Evaluations and the Compositional Structure of the Bar Construction
Carmen Constantin, Paolo Perrone, Tobias Fritz +1
The algebraic expression can be evaluated to , but it can also be partially evaluated to . In categorical algebra, such partial evaluations can be defined in…