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Register a new userAlgebras for enriched $infty$-operads
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Authors
Rune Haugseng
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Using the description of enriched $infty$-operads as associative algebras in symmetric sequences, we define algebras for enriched $infty$-operads as certain modules in symmetric sequences. For $mathbf{V}$ a nice symmetric monoidal model category, we prove that strict algebras for $Sigma$-cofibrant operads in $mathbf{V}$ are equivalent to algebras in the associated symmetric monoidal $infty$-category in this sense. We also show that $mathcal{O}$-algebras in $mathcal{V}$ can equivalently be described as morphisms of $infty$-operads from $mathcal{O}$ to endomorphism operads of (families of) objects of $mathcal{V}$.
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