A V-enriched ∞-operad is equivalent to a presentably symmetric monoidal V-module category generated by a ⊗-atomic marking of its colors.
Symmetric sequences,∞-operads, and the universal Lie algebra
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The spectral Lie operad is characterized by the free functor Sp to Lie(Sp) being symmetric monoidal with respect to an analog of the smash product.
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Enriched $\infty$-operads as marked algebras
A V-enriched ∞-operad is equivalent to a presentably symmetric monoidal V-module category generated by a ⊗-atomic marking of its colors.
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A characterization of the spectral Lie operad
The spectral Lie operad is characterized by the free functor Sp to Lie(Sp) being symmetric monoidal with respect to an analog of the smash product.