Semi-cosimplicial objects and spreadability. (English) Zbl 1401.18039

Evans, D. Gwion; Gohm, Rolf; Köstler, Claus

Rocky Mt. J. Math. 47, No. 6, 1839-1873 (2017).

Summary: 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.

MSC:

18G30	Simplicial sets; simplicial objects in a category (MSC2010)
20F36	Braid groups; Artin groups
46L53	Noncommutative probability and statistics

Keywords:

semi-cosimplicial object; coface operator; partial shift; braid monoid; cohomology; noncommutative probability space; spreadability; subfactor