Beck-Chevalley Conditions in Simplicial Sets

TL;DR

This paper introduces Skvortsov-Shehtman complexes, a special class of simplicial sets, providing examples that are not Kan complexes, and explores their properties within the context of simplicial set theory.

Contribution

It defines Skvortsov-Shehtman complexes and provides the first example of such a complex that is not a Kan complex, expanding the understanding of simplicial set structures.

Findings

Introduction of Skvortsov-Shehtman complexes

First example of a non-Kan Skvortsov-Shehtman complex

Analysis of properties distinguishing these complexes

Abstract

We describe certain class of simplicial sets introduced by Dmitry Skvortsov and Valentin Shehtman; we call such simplicial sets Skvortsov-Shehtman complexes. An example of a Skvortsov-Shehtman complex that is not a Kan complexes is given.