Simplicial methods in the resource theory of contextuality

Abstract: We introduce the concept of a category of scenarios structured over a monad with a gluing operator. Our main examples are the category of simplicial bundle scenarios and the category of stochastic bundle scenarios. Using a relative variant of the Grothendieck construction, we define the simplicial distribution functor, which extends the functor of empirical models. Finally, we leverage contextuality to characterize the convex maps between simplicial distributions, which are convex combinations of maps induced by morphisms in the category of simplicial bundle scenarios.

algebraic topologycategory theory

Audience: researchers in the topic

Bilkent Topology Seminar

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