Schreier split extensions of preordered monoids

Properties of preordered monoids are investigated and important subclasses of such structures are studied. The corresponding full subcategories of the category of preordered monoids are functorially related between them as well as with the categories of preordered sets and monoids. Schreier split extensions are described in the full subcategory of preordered monoids whose preorder is determined by the corresponding positive cone.