McKenzie–Hobby tame congruence theory

Summary

Tame congruence theory is a structure theory for finite algebras and locally finite varieties, developed by David Hobby and Ralph McKenzie. It studies each covering pair $\alpha \prec \beta$ in the congruence lattice of a finite algebra through the polynomial operations restricted to small subsets, the minimal sets. On these subsets the algebra behaves in one of five ways, which gives each covering pair a type: unary, affine, Boolean, lattice or semilattice. The types that occur in a locally finite variety control its congruence lattices and its Mal'cev conditions. For example, a locally finite variety omits the unary type exactly when it has a Taylor term.