Semi-Cosimplicial Objects and Spreadability

Abstract

To a semi-cosimplicial object (SCO) in a category we associate a system of partial shifts on the inductive limit. We show how to produce an SCO from an action of the infinite braid monoid $\mathbb{B}^+_\infty$ and provide examples. In categories of (noncommutative) probability spaces SCOs correspond to spreadable sequences of random variables, hence SCOs can be considered as the algebraic structure underlying spreadability.

20 pages, minor changes (1.2, 2.9, 4.3) in (v3), to be published in: Rocky Mountain Journal of Mathematics