Piecewise Boolean algebras and their domains

TL;DR

This paper characterizes piecewise Boolean domains and provides equivalent descriptions of the category of piecewise Boolean algebras through domain theory and sheaf theory, advancing the mathematical understanding of these structures.

Contribution

It introduces a characterization of piecewise Boolean domains and establishes their equivalence with structured sheaves and oriented domains, offering new perspectives on their categorical structure.

Findings

Characterization of piecewise Boolean domains

Equivalence between piecewise Boolean algebras and structured sheaves

New categorical descriptions of piecewise Boolean algebras

Abstract

We characterise piecewise Boolean domains, that is, those domains that arise as Boolean subalgebras of a piecewise Boolean algebra. This leads to equivalent descriptions of the category of piecewise Boolean algebras: either as piecewise Boolean domains equipped with an orientation, or as full structure sheaves on piecewise Boolean domains.