Semidirect products and crossed modules in monoids with operations

DOI10.1016/J.JPAA.2012.06.022zbMath1277.18016OpenAlexW1987917928MaRDI QIDQ1946172

Andrea Montoli, Nelson Martins-Ferreira, Manuela Sobral

Publication date: 18 April 2013

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2012.06.022

Mathematics Subject Classification ID

Nonabelian homological algebra (category-theoretic aspects) (18G50) Connections of semigroups with homological algebra and category theory (20M50) Equational classes, universal algebra in model theory (03C05) Categories of algebras (08C05) Groupoids, semigroupoids, semigroups, groups (viewed as categories) (18B40)

Related Items (24)

A survey of Schreier-type extensions of monoids ⋮ Baer sums of special Schreier extensions of monoids ⋮ \(\lambda\)-semidirect products of inverse monoids are weakly Schreier extensions ⋮ Two characterisations of groups amongst monoids ⋮ Cancellative conjugation semigroups and monoids ⋮ Intrinsic Schreier split extensions ⋮ Intrinsic Schreier special objects ⋮ Some notes on crossed semimodules ⋮ S-protomodularity of the category of cocommutative bialgebras ⋮ Weakly Schreier extensions for general algebras ⋮ A characterization of weakly Schreier extensions of monoids ⋮ Unnamed Item ⋮ The Nine Lemma and the push forward construction for special Schreier extensions of monoids with operations ⋮ Artin glueings of frames as semidirect products ⋮ On the ``Smith is Huq condition in \(S\)-protomodular categories ⋮ Quotients of monoid extensions and their interplay with Baer sums ⋮ On the categorical behaviour of preordered groups ⋮ Semidirect products and split short five lemma in normal categories ⋮ Crossed modules of monoids. I: Relative categories ⋮ Schreier split extensions of preordered monoids ⋮ Schreier split epimorphisms between monoids. ⋮ Split extensions and semidirect products of unitary magmas ⋮ Monoid extensions and the Grothendieck construction ⋮ Actor of a crossed module of dialgebras via tetramultipliers

Cites Work

• On categories with semidirect products
• Semidirect products of internal groupoids
• Cohomologie non abelienne de structures algébriques
• Obstruction theory in algebraic categories. I
• Extensions, crossed modules and internal categories in categories of groups with operations
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