2025/02/24 by Francesca Pratali, Pratali, Francesca
Mathematics · #05C05 #18N40 #18N45 #18N70 #55P48 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2502.17415
openalex publication_date 2025/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a discrete colored operad P, we construct an adjunction between the category of dendroidal sets over the nerve of P and the category of simplicial P-algebras, and prove that when P is Σ-free it establishes a Quillen equivalence with respect to the covariant model structure on the former category and the projective model structure on the latter. When P=A is a discrete category, this recovers a Quillen equivalence previously established by Heuts-Moerdijk, of which we provide an independent proof. To prove the constructed adjunction is a Quillen equivalence, we show that the left adjoint presents a previously established operadic straightening equivalence between ∞-categories. This involves proving that, for a discrete symmetric monoidal category A, the Heuts-Moerdijk equivalence is a monoidal equivalence of monoidal Quillen model categories.