Segal objects and the Grothendieck construction

· 2016 · math.AT · arXiv 1605.00706

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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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math.AT · 2025-01-09 · accept · novelty 5.0

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

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A straightening-unstraightening equivalence for $\infty$-operads math.AT · 2025-01-09 · accept · none · ref 4 · internal anchor
For any Lurie infinity-operad, the infinity-category of operadic left fibrations is equivalent to the infinity-category of algebras in spaces.