302 citations · 2.7k across the 73 of their papers we have counts for
6 papers · 1 filter
Infinite products and zero-one laws in categorical probability
Tobias Fritz, Eigil Fjeldgren Rischel
Markov categories are a recent category-theoretic approach to the foundations of probability and statistics. Here we develop this approach further by treating infinite products and…
Monotone additive statistics on heavy-tailed convolution semigroups
Tobias Fritz, Xiaosheng Mu, Omer Tamuz
We study sub-semigroups of the semigroup of probability measures on and monotone additive statistics on them, by which we mean maps to the reals that are monotone with…
Probability, valuations, hyperspace: Three monads on Top and the support as a morphism
Tobias Fritz, Paolo Perrone, Sharwin Rezagholi
We consider three monads on Top, the category of topological spaces, which formalize topological aspects of probability and possibility in categorical terms. The first one is the H…
A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics
Tobias Fritz
We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs. This means that we treat the following…
The universal property of infinite direct sums in C-categories and W-categories
Tobias Fritz, Bas Westerbaan
When formulating universal properties for objects in a dagger category, one usually expects a universal property to characterize the universal object up to unique unitary isomorphi…
A unified construction of semiring-homomorphic graph invariants
Tobias Fritz
It has recently been observed by Zuiddam that finite graphs form a preordered commutative semiring under the graph homomorphism preorder together with join and disjunctive product…