3 citations · 3 across the 3 of their papers we have counts for
6 papers · 1 filter
Convergence of martingales via enriched dagger categories
Paolo Perrone, Ruben Van Belle
We provide a categorical proof of convergence for martingales and backward martingales in mean, using enriched category theory. The enrichment we use is in topological spaces, with…
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…
Lifting couplings in Wasserstein spaces
Paolo Perrone
This paper makes mathematically precise the idea that conditional probabilities are analogous to path liftings in geometry. The idea of lifting is modelled in terms of the category…
Categorical algebra of conditional probability
Mika Bohinen, Paolo Perrone
In the field of categorical probability, one uses concepts and techniques from category theory, such as monads and monoidal categories, to study the structures of probability and s…
How to Represent Non-Representable Functors
Paolo Perrone
The arrows of a category are elements of particular sets, the hom-sets. These sets are functorial, and their functoriality specifies how to compose the arrows with other arrows of…
Notes on Category Theory with examples from basic mathematics
Paolo Perrone
These notes were originally developed as lecture notes for a category theory course. They should be well-suited to anyone that wants to learn category theory from scratch and has a…