A V-enriched ∞-operad is equivalent to a presentably symmetric monoidal V-module category generated by a ⊗-atomic marking of its colors.
A monadicity theorem for higher algebraic structures
5 Pith papers cite this work. Polarity classification is still indexing.
5
Pith papers citing it
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Introduces Goncharov Lie coalgebra from GL homology and uses it with spectral sequences to describe rational K-theory of fields via weight-3 polylogarithms beyond prior low-degree cases.
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.
Inverting endomorphism categories produces a stable homotopy theory of higher categories in which categorical spectra classify homology theories via a categorical Brown representability theorem.
Defines categorical homology via an Eilenberg-Steenrod analogue, proves a Dold-Kan correspondence using the Street nerve, and derives a Dold-Thom theorem for multiplicative structure and globe computations.
citing papers explorer
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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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The Goncharov Lie coalgebra of a field
Introduces Goncharov Lie coalgebra from GL homology and uses it with spectral sequences to describe rational K-theory of fields via weight-3 polylogarithms beyond prior low-degree cases.
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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.
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Stable homotopy theory of higher categories
Inverting endomorphism categories produces a stable homotopy theory of higher categories in which categorical spectra classify homology theories via a categorical Brown representability theorem.
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Homology of higher categories
Defines categorical homology via an Eilenberg-Steenrod analogue, proves a Dold-Kan correspondence using the Street nerve, and derives a Dold-Thom theorem for multiplicative structure and globe computations.