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.