Equivalence of Operads over Symmetric Monoidal Categories

2018/06/22 by Miradain Atontsa Nguemo, Nguemo, Miradain Atontsa
Mathematics · Medicine · #18D10 (Secondary) #18D50 #55U15 #55U35 (Primary) #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Pituitary Gland Disorders and Treatments

paper · pdf · doi:10.48550/arxiv.1806.08577

openalex publication_date 2018/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study conditions for extending Quillen model category properties , between two symmetric monoidal categories, to their associated category of symmetric sequences and of operads. Given a Quillen equivalence λ: C=Ch_\Bbbk,t \leftrightarrows D: R, so that D is any symmetric monoidal category and the adjoint pair (λ, R) is weak monoidal, we prove that the categories of connected operads Op_C and Op_D are Quillen equivalent. This expands an analogous result of Schwede-Shipley(\citeSS03) when we replace these categories of operads with the sub-categories of C-Monoid and D-monoid.

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