Taylor term

Summary

A Taylor term is an idempotent term with one identity in two variables $x, y$ for each argument place. The identity for a place has $x$ in that place on one side and $y$ in that place on the other side. Having a Taylor term is one of the weakest nontrivial Mal'cev conditions. For an idempotent variety, having a Taylor term means that no nontrivial algebra in the variety has only projections as term operations. It is central in the algebraic approach to constraint satisfaction. There, a finite core structure has a polynomial-time problem when its idempotent polymorphisms include a Taylor operation. Otherwise its problem is NP-complete.