The author unifies classical and derived bar and cobar constructions via twisted arrow categories of infinity-operads, giving new existence proofs and recovering classical comparison maps.
Sweedler Theory for (co)algebras and the bar-cobar constructions
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abstract
We prove that the category of dg-coalgebras is symmetric monoidal closed and that the category of dg-algebras is enriched, tensored, cotensored and strongly monoidal over that of coalgebras. We apply this formalism to reconstruct several known adjunctions, notably the bar-cobar adjunction.
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2025 1verdicts
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Lectures on bar and cobar
The author unifies classical and derived bar and cobar constructions via twisted arrow categories of infinity-operads, giving new existence proofs and recovering classical comparison maps.