Semi-cosimplicial objects and spreadability

Gwion Evans, Rolf Gohm, Claus Michael Köstler

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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 𝔹+∞ 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.
Original languageEnglish
Pages (from-to)1839-1873
Number of pages35
JournalRocky Mountain Journal of Mathematics
Issue number6
Early online date14 Mar 2016
Publication statusPublished - 21 Nov 2017


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


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