Geodesic
Cartesian fibrations and representability
Homology, homotopy, and applications, Tome 24 (2022) no. 2, pp. 135-161.

Voir la notice de l'article provenant de la source International Press of Boston

We use the complete Segal approach to the theory of Cartesian fibrations we developed previously to define and study representable Cartesian fibrations, generalizing representable right fibrations which have played a key role in $\infty$-category theory. In particular, we give a construction of representable Cartesian fibrations using over-categories and prove the Yoneda lemma for representable Cartesian fibrations, which generalizes the established Yoneda lemma for right fibrations. We then use the theory of Cartesian fibrations to study complete Segal objects internal to an $\infty$-category. Concretely, we prove the fundamental theorem of complete Segal objects, which characterizes equivalences of complete Segal objects. Finally we give two applications of the results. First, we present a method to construct Segal objects and second we study the representability of the universal co-Cartesian fibration.
DOI : 10.4310/HHA.2022.v24.n2.a7
Classification : 18F20
Keywords: higher category theory, Cartesian fibration, internal ∞-category, complete Segal object 
@article{HHA_2022_24_2_a6,
     author = {Nima Rasekh},
     title = {Cartesian fibrations and representability},
     journal = {Homology, homotopy, and applications},
     pages = {135--161},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2022},
     doi = {10.4310/HHA.2022.v24.n2.a7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n2.a7/}
}
TY  - JOUR
AU  - Nima Rasekh
TI  - Cartesian fibrations and representability
JO  - Homology, homotopy, and applications
PY  - 2022
SP  - 135
EP  - 161
VL  - 24
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n2.a7/
DO  - 10.4310/HHA.2022.v24.n2.a7
LA  - en
ID  - HHA_2022_24_2_a6
ER  - 
%0 Journal Article
%A Nima Rasekh
%T Cartesian fibrations and representability
%J Homology, homotopy, and applications
%D 2022
%P 135-161
%V 24
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n2.a7/
%R 10.4310/HHA.2022.v24.n2.a7
%G en
%F HHA_2022_24_2_a6
Nima Rasekh. Cartesian fibrations and representability. Homology, homotopy, and applications, Tome 24 (2022) no. 2, pp. 135-161. doi : 10.4310/HHA.2022.v24.n2.a7. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n2.a7/

Cité par Sources :