A categorical equivalence for odd or even involutive FLe-chains

Abstract

We lift the representation of the class I01c of odd or even involutive FLe-chains by the class BG of bunches of layer groups (a class of direct systems of abelian o-groups) published in [10], to a categorical equivalence between the category I01c of odd or even involutive FLe-chains equipped with their normal homomorphisms and the category BG of bunches of layer groups equipped with bunch homomorphisms, defined here. Restricting this equivalence only to odd or only to even involutive FLe-chains or to further subclasses thereof (e.g. to Sugihara chains) yields further categorical equivalences.