Free algebras and automata realizations in the language of categories
Jiřı́ Adámek · Czech digital mathematics library · 1974
Given a functor Ft 2C-*> JCthe category of P -algebras is formed as a generalization of universal algebras* The paper exhibits a construction of free F-al gebras and a discussion of its convergence.These results are applied to realizations of behaviours by automata in ca tegories, as defined by Arbib and Manes.We solve their pro blem: when do minimal realizations exist.A necessary and sufficient condition (under additional assumptions) is that F preserves co-meets of quotient objects (=-pushouts of epimorphisms).A stronger result is.obtained for normal functors.