Sheaves from Factor Congruences

Abstract

Factor congruences come from the product decompositions of an algebra. Using only them, rather than arbitrary congruences, creates a sheaf such that the algebra is isomorphic to the algebra of all global sections of the sheaf, not just to a subalgebra, as in the last chapter.The first section studies when there is a Boolean lattice of some of the factor congruences, and the third restricts attention to where all the factor congruences form a Boolean algebra.In between, many ways to identify algebras with Boolean lattices of factor congruences are found.The chapter closes with categorical equivalences between these classes of algebras and their sheaves.