2025/01/09 by Francesca Pratali, Pratali, Francesca
Mathematics · Medicine · #18N45 #18N55 #18N70 #55P48 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Pituitary Gland Disorders and Treatments
paper · pdf · doi:10.48550/arxiv.2501.05263
openalex publication_date 2025/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide a straightening-unstraightening adjunction for ∞-operads in Lurie's formalism, and show it establishes an equivalence between the ∞-category of operadic left fibrations over an ∞-operad O^⊗ and the ∞-category of O^⊗-algebras in spaces. In order to do so, we prove that the Hinich-Moerdijk comparison functors induce an equivalence between the ∞-categories of operadic left fibrations and dendroidal left fibrations over an ∞-operad, and we characterize, for any symmetric monoidal ∞-category C^⊗, the essential image of the monoidal unstraightening functor restricted to strong monoidal functors C^⊗→ S^×.