Constellations with range and IS-categories

Constellations are asymmetric generalisations of categories. Although they not required to possess a notion range, many natural examples do. These include commonly occurring constellations related concrete categories (since model surjective morphisms), and also others arising from quite different sources, including well-studied classes semigroups . We show how with well-behaved range operation nothing but ordered restrictions. characterise abstractly those that canonical extensions as so-called IS-categories. Such contain distinguished subcategories insertions (which monomorphisms) surjections (in general the epimorphisms) such each morphism admits unique factorisation into surjection followed by an insertion. Most familiar IS-categories, we some well-known properties these arise fact For appropriate choices morphisms in each, category IS-categories is shown be equivalent range.