In universal algebra, a clone is a set C of finitary operations on a set A such that The question whether clones should contain nullary operations or not is not treated uniformly in the literature.
[7][8] Given an algebra in a signature σ, the set of operations on its carrier definable by a σ-term (the term functions) is a clone.
The lattice of clones on a two-element set is countable,[9][10][3]: 39 and has been completely described by Emil Post[11][10] (see Post's lattice,[3]: 37 which traditionally does not show clones with nullary operations).
Conversely every abstract clone determines an algebraic theory with an n-ary operation for each element of Cn.
Every abstract clone C induces a Lawvere theory in which the morphisms m → n are elements of (Cm)n. This induces a bijective correspondence between Lawvere theories and abstract clones.