Direct Limits of Pseudoeffect Algebras

Abstract

This paper considers direct limits for the categories of pseudo effect algebras. For a category with pseudo effect algebras as objects and pseudo effect algebra-morphisms as morphisms, its direct limit exists in the same category. For a category with pseudo effect algebras as objects, and pseudo effect algebra-monomorphisms as morphisms, its direct limit exists in the same category. Moreover, when objects are lattice ordered pseudo effect algebras, byselecting suitable morphisms, some properties similar to those for the category of orthomodular lattices are obtained.