Free algebras, input processes and free monads
Věra Trnková, Jiřı́ Adámek, Vácłav Koubek, Jan Reiterman · Czech digital mathematics library · 1975
Given a functor F: X-• % , a category of F-algebras is defined and the existence of free F-algebras is discussed.This yields, under general conditions a characterization of input processes in the sense of Arbib, Manes or of free monads in the sense of Barr.The characterization is very simple: if F preserves monies then it is an input process iff for every object A there exists an object B with B a A v FB .