Geodesic
A note on the categorical notions of normal subobject and of equivalence class
Theory and applications of categories, The Rosebrugh Festschrift, Tome 36 (2021), pp. 65-101

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

In a non-pointed category E, a subobject which is normal to an equivalence relation is not necessarily an equivalence class. We elaborate this categorical distinction, with a special attention to the Mal'tsev context. Moreover, we introduce the notion of fibrant equipment, and we use it to establish some conditions ensuring the uniqueness of an equivalence relation to which a given subobject is normal, and to give a description of such a relation.

Publié le :
Classification : 18A32, 18C05, 18D30, 18E13, 08A30, 20J99
Keywords: normal subobject, equivalence class, connected pair of equivalence relations, unital, Mal'tsev and protomodular categories 
@article{TAC_2021_36_a2,
     author = {Dominique Bourn and Giuseppe Metere},
     title = {A note on the categorical notions of normal subobject and of equivalence class},
     journal = {Theory and applications of categories},
     pages = {65--101},
     publisher = {mathdoc},
     volume = {36},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2021_36_a2/}
}
TY  - JOUR
AU  - Dominique Bourn
AU  - Giuseppe Metere
TI  - A note on the categorical notions of normal subobject and of equivalence class
JO  - Theory and applications of categories
PY  - 2021
SP  - 65
EP  - 101
VL  - 36
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2021_36_a2/
LA  - en
ID  - TAC_2021_36_a2
ER  - 
%0 Journal Article
%A Dominique Bourn
%A Giuseppe Metere
%T A note on the categorical notions of normal subobject and of equivalence class
%J Theory and applications of categories
%D 2021
%P 65-101
%V 36
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2021_36_a2/
%G en
%F TAC_2021_36_a2
Dominique Bourn; Giuseppe Metere. A note on the categorical notions of normal subobject and of equivalence class. Theory and applications of categories, The Rosebrugh Festschrift, Tome 36 (2021), pp. 65-101. http://geodesic.mathdoc.fr/item/TAC_2021_36_a2/