Geodesic
Lax Colimits and Free Fibrations in $\infty$-Categories
Documenta mathematica, Tome 22 (2017), pp. 1225-1266
Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

We define and discuss lax and weighted colimits of diagrams in ∞-categories and show that the coCartesian fibration corresponding to a functor is given by its lax colimit. A key ingredient, of independent interest, is a simple characterization of the free Cartesian fibration on a functor of ∞-categories. As an application of these results, we prove that 2-representable functors are preserved under exponentiation, and also that the total space of a presentable Cartesian fibration between is presentable, generalizing a theorem of Makkai and Paré to the ∞-categories setting. Lastly, in an appendix, we observe that pseudofunctors between (2,1)-categories give rise to functors between ∞-categories via the Duskin nerve. setting and the Duskin nerve.
DOI : 10.4171/dm/593
Classification : 18A30, 18D30
Mots-clés : fibered categories, presentable categories, lax limits and colimits 
@article{10_4171_dm_593,
     author = {Rune Haugseng and David Gepner and Thomas Nikolaus},
     title = {Lax {Colimits} and {Free} {Fibrations} in $\infty${-Categories}},
     journal = {Documenta mathematica},
     pages = {1225--1266},
     year = {2017},
     volume = {22},
     doi = {10.4171/dm/593},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/593/}
}
TY  - JOUR
AU  - Rune Haugseng
AU  - David Gepner
AU  - Thomas Nikolaus
TI  - Lax Colimits and Free Fibrations in $\infty$-Categories
JO  - Documenta mathematica
PY  - 2017
SP  - 1225
EP  - 1266
VL  - 22
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/593/
DO  - 10.4171/dm/593
ID  - 10_4171_dm_593
ER  - 
%0 Journal Article
%A Rune Haugseng
%A David Gepner
%A Thomas Nikolaus
%T Lax Colimits and Free Fibrations in $\infty$-Categories
%J Documenta mathematica
%D 2017
%P 1225-1266
%V 22
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/593/
%R 10.4171/dm/593
%F 10_4171_dm_593
Rune Haugseng; David Gepner; Thomas Nikolaus. Lax Colimits and Free Fibrations in $\infty$-Categories. Documenta mathematica, Tome 22 (2017), pp. 1225-1266. doi: 10.4171/dm/593

Cité par Sources :