Titlebook: Higher Segal Spaces; Tobias Dyckerhoff,Mikhail Kapranov Book 2019 Springer Nature Switzerland AG 2019 Higher category theory.Segal Spaces.

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Hall Algebras Associated to 2-Segal Spaces,vers various variants of Hall algebras, such as classical Hall algebras, derived Hall algebras, and motivic Hall algebras. Applying a theory with transfer to other 2-Segal spaces, we obtain classically known algebras, such as Hecke algebras, but also new algebras, such as the ones associated to the cyclic nerve of a category.

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https://doi.org/10.1007/978-3-030-27124-4Higher category theory; Segal Spaces; 2-Segal property; 2-Segal spaces; 1-Segal spaces; pre-category obje

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Preliminaries,We recall some aspects of the basic categorical concepts of limits and Kan extensions. For more background on this classical material.

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The Path Space Criterion for 2-Segal Spaces,The main result of this chapter is Theorem 6.3.2 which expresses the 2-Segal condition for a simplicial object . in terms of 1-Segal conditions for simplicial analogs of the path space of ., as defined by Illusie.

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2-Segal Spaces from Higher Categories,All simplicial spaces in this section will be combinatorial, i.e., objects of ..