Free power-slim groupoids

Abstract

A power-slim groupoid is a groupoid that has the property: each of its mono-generated subgroupoids satisfies the identity [Formula: see text]. The class [Formula: see text] of power-slim groupoids is a variety. A description of free objects in this variety and a characterization of [Formula: see text]-free groupoids by means of [Formula: see text]-injective groupoids are obtained. It is shown that the class of [Formula: see text]-injective groupoids and the class of [Formula: see text]-free groupoids are hereditary.