Intrinsic Schreier split extensions

Andrea Montoli;Diana Rodelo;Van der Linden, Tim
(2020) Applied Categorical Structures — Vol. 28, n° 3, p. 517-538 (2020)

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Authors
  • Andrea MontoliUniversita' degli Studi di Milano
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  • Diana RodeloUniversidade do Algarve
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  • Van der Linden, Timorcid-logoUCLouvain
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Abstract
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.
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Andrea Montoli, Diana Rodelo, & Van der Linden, T. (2020). Intrinsic Schreier split extensions. Applied Categorical Structures, 28(3), 517-538. https://doi.org/10.1007/s10485-019-09588-4 (Original work published 2020)