This paper provides a bundle perspective to contextuality by introducing new
categories of contextuality scenarios based on bundles of simplicial complexes
and simplicial sets. The former approach generalizes earlier work on the
sheaf-theoretic perspective on contextuality, and the latter extends simplicial
distributions, a more recent approach to contextuality formulated in the
language of simplicial sets. After constructing our bundle categories, we also
construct functors that relate them and natural isomorphisms that allow us to
compare the notions of contextuality formulated in two languages. We are
motivated by applications to the resource theory of contextuality, captured by
the morphisms in these categories. In this paper, we develop the main formalism
and leave applications to future work.Comment: 50 pages, 2 figure