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 
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     title = {A {Model} for the {Higher} {Category} of {Higher} {Categories}},
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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/