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 [21]. 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.

Intrinsic Schreier special objects / A. Montoli, D. Rodelo, T. VAN DER LINDEN. - In: THEORY AND APPLICATIONS OF CATEGORIES. - ISSN 1201-561X. - 36:18(2021), pp. 514-555.

Intrinsic Schreier special objects

A. Montoli
Primo
;
2021

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 [21]. 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.
2-Engel group, Lie algebra; approximate operation; Imaginary morphism; Jónsson-Tarski variety; monoid; regular, unital, protomodular category;
Settore MAT/02 - Algebra
Settore MAT/01 - Logica Matematica
2021
Article (author)
File in questo prodotto:
File Dimensione Formato  
Montoli-Rodelo-Van der Linden, Intrinsic Schreier special objects.pdf

accesso riservato

Tipologia: Publisher's version/PDF
Dimensione 645.12 kB
Formato Adobe PDF
645.12 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/928259
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact