28 citations · 159 across the 26 of their papers we have counts for
4 papers · 1 filter
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…
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…
De Finetti's Theorem in Categorical Probability
Tobias Fritz, Tomáš Gonda, Paolo Perrone
We present a novel proof of de Finetti's Theorem characterizing permutation-invariant probability measures of infinite sequences of variables, so-called exchangeable measures. The…
Kan extensions are partial colimits
Paolo Perrone, Walter Tholen
One way of interpreting a left Kan extension is as taking a kind of "partial colimit", whereby one replaces parts of a diagram by their colimits. We make this intuition precise by…