Centre for Mathematics, University of Coimbra

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Type:	Preprint
National /International:	International
Title:	Intrinsic Schreier special objects
Publication Date:	2021-02-07
Authors:	- Andrea Montoli - Diana Rodelo - Tim Van der Linden
Abstract:	Motivated by the categorical-algebraic analysis of split epimorphisms of monoids, we study the concept of a special object induced by the intrinsic Schreier split epimorphisms in the context of a regular unital category with binary coproducts, comonadic covers and a natural imaginary splitting in the sense of our article [20]. In this context, each object comes naturally equipped with an imaginary magma structure. We analyse the intrinsic Schreier split epimorphisms in this setting, showing that their properties improve when the imaginary magma structures happen to be associative. We compare the intrinsic Schreier special objects with the protomodular objects, and characterise them in terms of the imaginary magma structure. We furthermore relate them to the Engel property in the case of groups and Lie algebras.
Institution:	DMUC 21-01
Online version:	http://www.mat.uc.pt...prints/eng_2021.html
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