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 in...

Among the most familiar systems in symbolic dynamics are the subshifts of finite type, or SFT’s for short. SFT’s are relatively easy to analyze, and have many pleasant properties such as intrinsic ergodicity and unique ergodicity with respect to the tail. A larger class, which has the desirable property of being closed under factors, is that of sofic systems. This class of systems retains many ...