ABSTRACT
We characterize in a relatively simple algebraic fashion the functors establishing categorical equivalence between two equational classes of algebras. Our results will actually be proved to hold for categorical equivalences between any two classes K https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203748671/73ba9466-413e-4e6d-b2c9-72a90d723427/content/eq1263.tif"/> and ℒ of finitary algebras where each of K https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203748671/73ba9466-413e-4e6d-b2c9-72a90d723427/content/eq1264.tif"/> and ℒ contains the finitely generated free algebras of the variety it generates, and is hereditary in the sense that it contains all subalgebras of its algebras. They can easily be extended to classes of infinitary algebras of bounded signature, where K https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203748671/73ba9466-413e-4e6d-b2c9-72a90d723427/content/eq1265.tif"/> and ℒ are assumed to be hereditary and to contain all their free algebras of ranks up to a common bound on the ranks of their operations.
