Contextuality is the failure of "local" probabilistic models to become global
ones. In this paper we introduce the notions of \emph{measurable fibre
bundles}, \emph{probability fibre bundles}, and \emph{sample fibre bundle}
which capture and make precise the former statement. The central notions of
contextuality are discussed under this formalism, examples worked out, and some
new aspects pointed out.Comment: 14 pages; no figures; Purdue-Winer Memorial Lectures 2018; submitted
to Phil. Trans. Roy. Soc. A. Comments are very welcom
