Lawvere Theory

A Lawvere theory is a small category with finite products whose objects are finite powers of a distinguished object (often indexed by natural numbers), used to present finitary single-sorted algebraic theories: operations are morphisms and equations are commuting diagrams.

A small category with finite products whose objects are finite powers of a distinguished object and whose product-preserving functors into Set correspond to models of a finitary algebraic theory; it encodes algebraic operations and equations categorically.