A CATEGORICAL CONSTRUCTION OF A VARIETY OF CLONE ALGEBRAS
George Voutsadakis · Scientiae mathematicae Japonicae · 2004
A category Cln representing free algebras of clones of operations of finite but arbitrary arities is constructed together with an adjunction 〈F,U, η, 〉 : Set → Cln. This gives rise to an algebraic theory T over Set. A single-sorted variety V of clone algebras is, then, equationally defined inspired by the multi-sorted construction of Taylor [20]. It is shown that the Eilenberg-Moore category of T-algebras is isomorphic to the category V corresponding to the variety V.