Segal objects and the Grothendieck construction

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arxiv 1605.00706 v2 pith:T3QK2PE7 submitted 2016-05-02 math.AT

Pedro Boavida de Brito This is my paper · ORCID

classification math.AT

keywords objectssegalbasiccategoricalcategoryconstructioncontextdiscuss

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abstract

We discuss right fibrations in the $\infty$-categorical context of Segal objects in a category V and prove some basic results about these.

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A straightening-unstraightening equivalence for $\infty$-operads
math.AT 2025-01 accept novelty 5.0 of 10

For any Lurie infinity-operad, the infinity-category of operadic left fibrations is equivalent to the infinity-category of algebras in spaces.