2 problems

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The Francis–Gaitsgory bar–cobar equivalence conjecture for augmented nilpotent algebras
Let $\mathcal{O}$ be an operad in a symmetric monoidal category $\mathcal{V}$ , and let $\mathsf{Bar}(\mathcal{O})$ be its bar cooperad. Write…
Conjectureopenbar-cobar-duality operadsarXiv posted 2 days ago
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Fresse's bar-cobar equivalence conjecture for $E_n$ -algebras
Let $A$ be an $4\mathcal E_n$ algebra, and let $B A$ denote its bar construction, regarded as an $4\mathcal E_{n-1}$ Hopf algebra. Let $\Omega B A$ be the cobar construction applie…
Conjectureopenbar-cobar-duality homotopical-algebra operadsarXiv posted 2 days ago

The Francis–Gaitsgory bar–cobar equivalence conjecture for augmented nilpotent algebras