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This paper provides a bundle perspective to contextuality by introducing newcategories of contextuality scenarios based on bundles of simplicial complexesand simplicial sets. The former approach generalizes earlier work on thesheaf-theoretic perspective on contextuality, and the latter extends simplicialdistributions, a more recent approach to contextuality formulated in thelanguage of simplicial sets. After constructing our bundle categories, we alsoconstruct functors that relate them and natural isomorphisms that allow us tocompare the notions of contextuality formulated in two languages. We aremotivated by applications to the resource theory of contextuality, captured bythe morphisms in these categories. In this paper, we develop the main formalismand leave applications to future work.

A bundle perspective on contextuality: Empirical models and simplicial distributions on bundle scenarios