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A survey of (\infty, 1)-categories

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arxiv math/0610239 v1 pith:PTQKDMNW submitted 2006-10-09 math.AT math.CT

Julia E. Bergner This is my paper · ORCID
classification math.ATmath.CT
keywords categorieshomotopydifferentinftymodelssegaltheorycomparisons
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In this paper we give a summary of the comparisons between different definitions of so-called (\infty,1)-categories, which are considered to be models for \infty-categories whose n-morphisms are all invertible for n>1. They are also, from the viewpoint of homotopy theory, models for the homotopy theory of homotopy theories. The four different structures, all of which are equivalent, are simplicial categories, Segal categories, complete Segal spaces, and quasi-categories.

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  1. Entanglement of Sections: The pushout of entangled and parameterized quantum information

    quant-ph 2023-09 unverdicted novelty 6.0 of 10

    The pushout of entangled and parameterized quantum information in monoidal categories yields the external tensor product on flat K-theory bundles.

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