Lifting amalgams and other colimits of monoids

Abstract

Let U = [{Mi: i ∈ I}; U; {øi: i ∈ I}] be a monoid amalgam of inclusions, i.e. U and each Mi is a monoid, and øi: U → Mi are inclusions. Let be the monoid free product of the amalgam U (see for example [10] for these concepts), and let β: B → H be a homomorphism of monoids. The type of question we seek to answer in this paper is under what conditions (on β, B and H) can we deduce that B is isomorphic to the free product of the amalgam