## Rocky Mountain Journal of Mathematics

#### 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.

#### Article information

Source
Rocky Mountain J. Math., Volume 47, Number 6 (2017), 1839-1873.

Dates
First available in Project Euclid: 21 November 2017

https://projecteuclid.org/euclid.rmjm/1511254955

Digital Object Identifier
doi:10.1216/RMJ-2017-47-6-1839

Mathematical Reviews number (MathSciNet)
MR3725247

Zentralblatt MATH identifier
06816573

#### Citation

Evans, D. Gwion; Gohm, Rolf; Köstler, Claus. Semi-cosimplicial objects and spreadability. Rocky Mountain J. Math. 47 (2017), no. 6, 1839--1873. doi:10.1216/RMJ-2017-47-6-1839. https://projecteuclid.org/euclid.rmjm/1511254955

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