BilTop | Igor Sikora | Equivariant contextuality

Simplicial quantum contextuality, introduced by Okay, Kharoof and Ipek, is a framework for using topological methods based on simplicial sets to study quantum contextuality. It subsumes earlier approaches - topological (Okay, Roberts, Bartlett, Raussendorf) and sheaf-theoretic (Abramsky, Brandenburger).
In this talk we will discuss how group action can be composed into this framework. To this end, we will use such tools as Borel construction and partial groups in the sense of Broto-Gonzalez. We will start with the notions of equivariant simplicial distributions and equivariant contextuality and connect them with the Borel construction. Then we will proceed with the cohomological aspects, which are based on the extensions of partial groups and cofibre sequences of simplicial sets.