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.
Koszul duality and a conjecture of Francis–Gaitsgory, arxiv.2408.06173
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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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On periodic homotopy and homology equivalences of spaces
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.
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Point-set models for homotopy coherent coalgebras
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.