Yoneda Lemma for Complete Segal Spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 2, pp. 3-38.

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In this note we formulate and give a self-contained proof of the Yoneda lemma for $\infty$-categories in the language of complete Segal spaces.
Keywords: simplicial sets, complete Segal spaces, Yoneda lemma.
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Ya. Varshavsky; D. A. Kazhdan. Yoneda Lemma for Complete Segal Spaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 2, pp. 3-38. http://geodesic.mathdoc.fr/item/FAA_2014_48_2_a0/

[1] P. Goerss, J. Jardine, Simplicial Homotopy Theory, Progress in Math., 174, Birkhäuser, Basel, 1999 | MR | Zbl

[2] D. Kazhdan, Y. Varshavsky, Yoneda lemma for complete Segal spaces, II, gotovitsya k pechati

[3] D. Kazhdan, Y. Varshavsky, Yoneda lemma for $(\infty,n)$-categories, gotovitsya k pechati

[4] J. Lurie, Higher Topos Theory, Annals of Math. Studies, 170, Princeton University Press, Princeton, NJ, 2009 | MR | Zbl

[5] J. Lurie http://www.math.harvard.edu/~lurie/papers/higheralgebra.pdf

[6] C. Rezk, “A model for the homotopy theory of homotopy theory”, Trans. Amer. Math. Soc., 353:3 (2001), 973–1007 | DOI | MR | Zbl

[7] C. Rezk, “A Cartesian presentation of weak $n$-categories”, Geom. Topol., 14:1 (2010), 521–571 | DOI | MR | Zbl

[8] C. Rezk, Fibrations and homotopy colimits of simplicial sheaves, 1998, arXiv: math/9811038

[9] D. Quillen, Homotopical algebra, Lecture Notes in Math., 43, Springer-Verlag, Berlin–New York, 1967 | DOI | MR | Zbl