Algebraic and locally algebraic functors

Many algebraic constructions can be viewed as algebra-valued functors. Using a category-theoretic formulation of universal algebra and first-order logic originated by F. W. Lawvere, we obtain algebraic and logical results concerning functors which correspond to important kinds of algebraic constructions--in particular, to Boolean powers and bounded Boolean powers. Morita equivalence is characterized for equational and locally equational classes of algebras as algebraic and locally algebraic categories.