Dario Stein: Categories of Relations which Compose Independently

Speaker: Dario Stein (Radboud University Nijmegen)

Abtract: Independence appears as an important notion in program semantics in various forms: separation for heaps in memory management, variation independence for databases, and (conditional) independence of random variables in probabilistic programming. While there exist various general theories of independence like semigraphoids, Alex Simpson has recently formulated a convenient new category-theoretic axiomatization based on the notion of an independent square.

I will discuss how such a notion of independence combines with constructions from categorical logic. Paralleling the equivalence between tabular allegories and regular categories, I will discuss a variant of the Rel-construction where relations compose by independent pullback. On the work in progress-side, I will discuss some insights and open questions into the theory of presheaves over independence categories, and the probabilistic separation logic LILAC (Li&al).

This talk is based on joint work with Alex Simpson, Matthew Di Meglio, Chris Heunen, JS Lemay and Paolo Perrone.