Split extensions and semidirect products of unitary magmas

Marino Gran; George Janelidze; Manuela Sobral

Commentationes Mathematicae Universitatis Carolinae (2019)

  • Volume: 60, Issue: 4, page 509-527
  • ISSN: 0010-2628

Abstract

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We develop a theory of split extensions of unitary magmas, which includes defining such extensions and describing them via suitably defined semidirect product, yielding an equivalence between the categories of split extensions and of (suitably defined) actions of unitary magmas on unitary magmas. The class of split extensions is pullback stable but not closed under composition. We introduce two subclasses of it that have both of these properties.

How to cite

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Gran, Marino, Janelidze, George, and Sobral, Manuela. "Split extensions and semidirect products of unitary magmas." Commentationes Mathematicae Universitatis Carolinae 60.4 (2019): 509-527. <http://eudml.org/doc/295072>.

@article{Gran2019,
abstract = {We develop a theory of split extensions of unitary magmas, which includes defining such extensions and describing them via suitably defined semidirect product, yielding an equivalence between the categories of split extensions and of (suitably defined) actions of unitary magmas on unitary magmas. The class of split extensions is pullback stable but not closed under composition. We introduce two subclasses of it that have both of these properties.},
author = {Gran, Marino, Janelidze, George, Sobral, Manuela},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {unitary magma; split extension; firm split extension; semidirect product},
language = {eng},
number = {4},
pages = {509-527},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Split extensions and semidirect products of unitary magmas},
url = {http://eudml.org/doc/295072},
volume = {60},
year = {2019},
}

TY - JOUR
AU - Gran, Marino
AU - Janelidze, George
AU - Sobral, Manuela
TI - Split extensions and semidirect products of unitary magmas
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2019
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 60
IS - 4
SP - 509
EP - 527
AB - We develop a theory of split extensions of unitary magmas, which includes defining such extensions and describing them via suitably defined semidirect product, yielding an equivalence between the categories of split extensions and of (suitably defined) actions of unitary magmas on unitary magmas. The class of split extensions is pullback stable but not closed under composition. We introduce two subclasses of it that have both of these properties.
LA - eng
KW - unitary magma; split extension; firm split extension; semidirect product
UR - http://eudml.org/doc/295072
ER -

References

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