Geodesic
Intrinsic Schreier special objects
Theory and applications of categories, The Rosebrugh Festschrift, Tome 36 (2021), pp. 514-555

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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 co-products, 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.

Publié le :
Classification : 20M32, 20J15, 18E13, 03C05, 08C05
Keywords: Imaginary morphism, approximate operation, regular, unital, protomodular category, monoid, 2-Engel group, Lie algebra, Jónsson-Tarski variety 
@article{TAC_2021_36_a17,
     author = {Andrea Montoli and Diana Rodelo and Tim Van der Linden},
     title = {Intrinsic {Schreier} special objects},
     journal = {Theory and applications of categories},
     pages = {514--555},
     publisher = {mathdoc},
     volume = {36},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2021_36_a17/}
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Andrea Montoli; Diana Rodelo; Tim Van der Linden. Intrinsic Schreier special objects. Theory and applications of categories, The Rosebrugh Festschrift, Tome 36 (2021), pp. 514-555. http://geodesic.mathdoc.fr/item/TAC_2021_36_a17/