Geodesic
A Model for the Higher Category of Higher Categories
Theory and applications of categories, Tome 41 (2024), pp. 21-70.

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

We use fibrations of complete Segal spaces as introduced in [Ras22, Ras23a] to construct four complete Segal spaces: Reedy fibrant simplicial spaces, Segal spaces, complete Segal spaces, and spaces. Moreover, we show each one comes with a universal fibration that classifies Reedy left fibrations, Segal coCartesian fibrations, coCartesian fibrations and left fibrations and prove these are representable fibrations in the sense of [Ras22]. Finally, we use equivalences between quasi-categories and complete Segal spaces constructed in [JT07, Ras21a] to present analogous constructions using fibrations of quasi-categories. As part of establishing the results, we also develop a theory of minimal Reedy fibrations for elegant Reedy categories, which can be of independent interest.
Publié le :
Classification : 18N60, 18N50, 55U35, 18N45, 18N40
Keywords: higher category theory, ∞-categories, complete Segal spaces, left fibrations, minimal fibrations 
@article{TAC_2024_41_a1,
     author = {Nima Rasekh},
     title = {A {Model} for the {Higher} {Category} of {Higher} {Categories}},
     journal = {Theory and applications of categories},
     pages = {21--70},
     publisher = {mathdoc},
     volume = {41},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a1/}
}
TY  - JOUR
AU  - Nima Rasekh
TI  - A Model for the Higher Category of Higher Categories
JO  - Theory and applications of categories
PY  - 2024
SP  - 21
EP  - 70
VL  - 41
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2024_41_a1/
LA  - en
ID  - TAC_2024_41_a1
ER  - 
%0 Journal Article
%A Nima Rasekh
%T A Model for the Higher Category of Higher Categories
%J Theory and applications of categories
%D 2024
%P 21-70
%V 41
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2024_41_a1/
%G en
%F TAC_2024_41_a1
Nima Rasekh. A Model for the Higher Category of Higher Categories. Theory and applications of categories, Tome 41 (2024), pp. 21-70. http://geodesic.mathdoc.fr/item/TAC_2024_41_a1/