Geodesic
Lax comma categories: cartesian closedness, extensivity, topologicity, and descent
Theory and applications of categories, Tome 41 (2024), pp. 516-530

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

We investigate the properties of lax comma categories over a base category X, focusing on topologicity, extensivity, cartesian closedness, and descent. We establish that the forgetful functor from Cat//X to Cat is topological if and only if X is large-complete. Moreover, we provide conditions for Cat//X to be complete, cocomplete, extensive and cartesian closed. We analyze descent in Cat//X and identify necessary conditions for effective descent morphisms. Our findings contribute to the literature on lax comma categories and provide a foundation for further research in 2-dimensional Janelidze's Galois theory.

Publié le :
Classification : 18N10, 18N15, 18A05, 18A22, 18A40
Keywords: lax comma categories, Grothendieck descent theory, Galois theory, 2-dimensional category theory, topological functor, effective descent morphism, cartesian closed category, exponentiability 
@article{TAC_2024_41_a15,
     author = {Maria Manuel Clementino and Fernando Lucatelli Nunes and Rui Prezado},
     title = {Lax comma categories: cartesian closedness, extensivity, topologicity,  and descent},
     journal = {Theory and applications of categories},
     pages = {516--530},
     publisher = {mathdoc},
     volume = {41},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a15/}
}
TY  - JOUR
AU  - Maria Manuel Clementino
AU  - Fernando Lucatelli Nunes
AU  - Rui Prezado
TI  - Lax comma categories: cartesian closedness, extensivity, topologicity,  and descent
JO  - Theory and applications of categories
PY  - 2024
SP  - 516
EP  - 530
VL  - 41
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2024_41_a15/
LA  - en
ID  - TAC_2024_41_a15
ER  - 
%0 Journal Article
%A Maria Manuel Clementino
%A Fernando Lucatelli Nunes
%A Rui Prezado
%T Lax comma categories: cartesian closedness, extensivity, topologicity,  and descent
%J Theory and applications of categories
%D 2024
%P 516-530
%V 41
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2024_41_a15/
%G en
%F TAC_2024_41_a15
Maria Manuel Clementino; Fernando Lucatelli Nunes; Rui Prezado. Lax comma categories: cartesian closedness, extensivity, topologicity,  and descent. Theory and applications of categories, Tome 41 (2024), pp. 516-530. http://geodesic.mathdoc.fr/item/TAC_2024_41_a15/