Canonical Objects in Classes of (n, V)-Groupoids

Abstract

AMS Subj. Classification: 03C05, 08B20Free algebras are very important in studying classes of algebras, especially varieties of algebras. Any algebra that belongs to a given variety of algebras can be characterized as a homomorphic image of a free algebra of that variety. Describing free algebras is an important task that can be quite complicated, since there is no general method to resolve this problem. The aim of this work is to investigate classes of groupoids, i.e. algebras with one binary operation, that satisfy certain identities or other conditions, and look for free objects in such classes