The category of MV-pairs

Abstract

An MV-pair is a pair (B,G), where B is a Boolean algebra and G is a subgroup of the automorphism group of B satisfying certain condition. Recently it was proved by one of the authors that for an MV-pair (B,G), G is an effect-algebraic congruence and B/G is an MV-algebra. Moreover, every MV-algebra M can be represented by an MV-pair in this way.

In this paper we show that one can define a suitable category of MV-pairs in such a way that there exist a faithful functor from the category of MV-algebras to the aforementioned category and a functor in the reversed direction.