Montoli, AndreaRodelo, DianaVan der Linden, Tim2020-07-242021-06-012020-060927-2852http://hdl.handle.net/10400.1/14169In the context of regular unital categories we introduce an intrinsic version of the notion of a Schreier split epimorphism, originally considered for monoids. We show that such split epimorphisms satisfy the same homological properties as Schreier split epimorphisms of monoids do. This gives rise to new examples of S-protomodular categories, and allows us to better understand the homological behaviour of monoids from a categorical perspective.engSemidirect productsMonoidsMaltsevLemmaFibration of pointsJointly extremal-epimorphic pairRegular categoryUnital categoryProtomodular categoryMonoidJónsson–Tarski varietyjournal article10.1007/s10485-019-09588-4