Gluing and extending simplicial distributions

Abstract: In the theory of simplicial distributions, contextuality is determined by a natural map. As a result, any diagram of measurement spaces induces a diagram that can be used to compare contextuality. In this talk, we will focus on two cases: (1) an Inclusion map between measurement spaces and (2) a pushout square of measurement spaces. These two cases lead to the Extending Lemma and the Gluing Lemma, respectively. The proof of the second Lemma is based on the fact that the distribution monad weakly preserves pullbacks: the natural map from the distribution of a pullback to the pullback of the distributions has a section. We will show that this section behaves like a composition.

(This talk is part of the reading seminar series on the theory and applications of simplicial distributions.)

algebraic topologycategory theory

Audience: researchers in the topic

Bilkent Topology Seminar

Series comments: Contact the organizer to get access to Zoom.

Recordings of talks available at www.youtube.com/channel/UCLrmyGpqxyeVpTcA1b5HcMw/videos