A V-enriched ∞-operad is equivalent to a presentably symmetric monoidal V-module category generated by a ⊗-atomic marking of its colors.
Koszul duality and a conjecture of Francis–Gaitsgory, arxiv.2408.06173
5 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Koszul duality is a fundamental correspondence between algebras for an operad $\mathcal{O}$ and coalgebras for its dual cooperad $B\mathcal{O}$, built from $\mathcal{O}$ using the bar construction. Francis-Gaitsgory proposed a conjecture about the general behavior of this duality. The main result of this paper, roughly speaking, is that Koszul duality provides an equivalence between the subcategories of nilcomplete algebras and conilcomplete coalgebras and that these are the largest possible subcategories for which such a result holds. This disproves Francis-Gaitsgory's prediction, but does provide an adequate replacement. We show that many previously known partial results about Koszul duality can be deduced from our results.
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2026 5representative citing papers
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.
Precise comparisons are established between T(n)-homology and v_n-periodic homotopy equivalences, including a T(n)-local version of Kuhn's result and a formula for L_n^f-localization of infinite loop spaces from spectra with L_{n-1}^f vanishing.
Localized dg-coalgebras over a field are equivalent to coalgebras over cofibrant enriched ∞-operads via induction on cell attachments, yielding point-set models for E_n-coalgebras and cellular chains.
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