[cancelled] Simplicial methods in the resource theory of contextuality

Abstract: In this talk, we introduce two categories: The category of event scenarios, which extends the standard scenarios known from the sheaf-theoretic approach. The category of scenarios over a monad with a gluing operation, which extends the category of simplicial bundle scenarios. We define the empirical model and simplicial distribution functors for these categories using the relative Grothendieck construction that presented in Behzat’s talk. We then introduce an internal hom structure for event scenarios and for simplicial bundle scenarios, which we call mapping scenarios. Finally, we present our main result, which characterizes convex maps between simplicial distributions in terms of non-contextual distributions on the corresponding mapping scenario, thereby enhancing and extending previous results in categorical quantum foundations.

algebraic topologycategory theory

Audience: researchers in the topic

Bilkent Topology Seminar

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