Lawvere theory
In category theory, a Lawvere theory (named after American mathematician William Lawvere) is a category that can be considered a categorical counterpart of the notion of an equational theory. Intuitively, it is a categorical generalization of algebraic structures (e.g., a group or a ring), where there exists a "generic" object and all objects are isomorphic to an integer power of x {\displaystyle x} , representing the inputs for the n {\displaystyle n} -ary operations on x {\displaystyle x} (i.e., of the form x n ↦ x {\displaystyle x^{n}\mapsto x} , starting from the fact that x := x 1 {\displaystyle x:=x^{1}} and so x ∘ x := x 1 ∘ x 1 := x 1 x 1 := x 2 {\displaystyle x\circ x:=x^{1}\circ x^{1}:=x^{1}x^{1}:=x^{2}} ; trivially generalizing inductively, we get the rest of the objects) where the operations come from the algebraic structure at hand (e.g., addition and/or multiplication).