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Keywords:
Homotopy Theory; Higher Category Theory
Homotopy Theory; Higher Category Theory
Summary:
The goal of this paper is to prove an equivalence between the $(\infty,2)$-category of {\it cartesian} factorization systems on $\infty$-categories and that of {\it pointed} cartesian fibrations of $\infty$-categories. This generalizes a similar result known for ordinary categories and sheds some light on the interplay between these two seemingly distant concepts.
References:
[1] Cisinski, Denis-Charles: Higher categories and homotopical algebra. Cambridge Studies in Advanced Mathematics, vol. 180, Cambridge University Press, Cambridge MR 3931682
[2] Gepner, David, Haugseng, Rune, Nikolaus, Thomas: Lax colimits and free fibrations in ∞-categories. Doc. Math. 22, 1225–1266 MR 3690268
[3] Joyal, André: Notes on quasi-categories. Preprint
[4] Lurie, Jacob: (∞,2)-categories and the Goodwillie Calculus I. Preprint
[5] Lurie, Jacob: Higher Topos Theory. Annals of Mathematics Studies, vol. 170, Princeton University Press, Princeton, NJ MR 2522659
[6] Riehl, E., Verity, D.: Fibrations and yoneda lemma in an ∞-cosmos. Journal of Pure and Applied Algebra 221, no. 3 MR 3556697
[7] Rosický, J., Tholen, W.: Factorization, fibration and torsion. Journal of Homotopy and Related Structures 355, no. 9, 3611–3623 MR 2369170
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