On strong homotopy for quasi-schemoids

2013/10/07 by Katsuhiko Kuribayashi, Kuribayashi, Katsuhiko
Mathematics · #Algebraic Topology (math.AT) #Category Theory (math.CT) #Combinatorics (math.CO) #FOS: Mathematics #math.AT #math.CO #math.CT

paper · pdf · doi:10.48550/arxiv.1310.1736

12 pages

arxiv created 2014/10/24 · arxiv updated 2014/10/27

Abstract

A quasi-schemoid is a small category with a particular partition of the set of morphisms. We define a homotopy relation on the category of quasi-schemoids and study its fundamental properties. As a homotopy invariant, the homotopy set of self-homotopy equivalences on a quasi-schemoid is introduced. The main theorem enables us to deduce that the homotopy invariant for the quasi-schemoid induced by a finite group is isomorphic to the automorphism group of the given group.

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