Equivalence of Operads over Symmetric Monoidal Categories

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 $\lambda :\mathcal{C}=C{h}_{\mathbb{k},t}\leftrightarrows \mathcal{D}:R,$ so that $\mathcal{D}$ is any symmetric monoidal category and the adjoint pair $(\lambda ,R)$ is weak monoidal, we prove that the categories of connected operads $O{p}_{\mathcal{C}}$ and $O{p}_{\mathcal{D}}$ are Quillen equivalent. This expands an analogous result of Schwede-Shipley(\cite{SS03}) when we replace these categories of operads with the sub-categories of $\mathcal{C}$-Monoid and $\mathcal{D}$-monoid.

References in corpus (1)

• Shrinkability, relative left properness, and derived base change