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On strong homotopy for quasi-schemoids

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Katsuhiko Kuribayashi

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. The homotopy set of
self-homotopy equivalences on a quasi-schemoid is used as a homotopy
invariant in the study. 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. %These
considerations are the first step to develop homotopy theory for
quasi-schemoids.

Keywords:
Association scheme, small category, schemoids, homotopy

2010 MSC:
18D35, 05E30, 55U35

*Theory and Applications of Categories,*
Vol. 30, 2015,
No. 1, pp 1-14.

Published 2015-01-07.

http://www.tac.mta.ca/tac/volumes/30/1/30-01.pdf

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