Intrinsic Schreier split extensions

Montoli, Andrea; Rodelo, Diana; Van der Linden, Tim

http://hdl.handle.net/10400.1/14169

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Authors

Montoli, Andrea

Rodelo, Diana

Van der Linden, Tim

Abstract(s)

In 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.

Keywords

Semidirect products Monoids Maltsev Lemma Fibration of points Jointly extremal-epimorphic pair Regular category Unital category Protomodular category Monoid Jónsson–Tarski variety