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Yoneda lemma for complete Segal spaces. (English. Russian original) Zbl 1310.18007
Funct. Anal. Appl. 48, No. 2, 81-106 (2014); translation from Funkts. Anal Prilozh. 48, No. 2, 3-38 (2014).
This article is a contribution to abstract homotopy theory. It deals with (complete) Segal spaces, which are a model for \(\infty\)-categories, introduced in [C. Rezk, Trans. Am. Math. Soc. 353, No. 3, 973–1007 (2001; Zbl 0961.18008)]. These objects are bisimplicial sets (called simplicial spaces in the paper) satisfying suitable conditions. The paper states and proves, in a self-contained way, a Yoneda embedding theorem for Segal spaces. The proof relies in part on a notion of quasi-fibration which is defined and studied in the third section of the article.
This paper is written in an efficient way, but the small number of examples, motivations or comparisons with other points of view on higher categories or related topics makes its precise interest hard to understand for the non-expert reader.

18G55 Nonabelian homotopical algebra (MSC2010)
18G30 Simplicial sets; simplicial objects in a category (MSC2010)
55P99 Homotopy theory
18A05 Definitions and generalizations in theory of categories
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[2] D. Kazhdan and Y. Varshavsky, ”Yoneda lemma for complete Segal spaces II” (in preparation). · Zbl 1310.18007
[3] D. Kazhdan and Y. Varshavsky, ”Yoneda lemma for ( n)-categories” (in preparation). · Zbl 1310.18007
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