Schreier split extensions of preordered monoids - Martins-Ferreira, Nelson; Sobral, Manuela (Journal of logical and algebraic methods in programming, 2021)
Properties of preordered monoids are investigated and important subclasses of such structures are studied. The corresponding full subcategories are related between them by appropriate functors as well as with the categories of preordered sets and of monoids. Schreier split extensions are described in the full subcategory of preordered monoids whose preorder is determined by the corresponding positive cone.