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Sweedler Theory for (co)algebras and the bar-cobar constructions

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arxiv 1309.6952 v1 pith:2XSXOKZL submitted 2013-09-26 math.CT math.ATmath.RA

Matthieu Anel , André Joyal This is my paper · ORCID
classification math.CTmath.ATmath.RA
keywords bar-cobarcategorymonoidaladjunctionadjunctionsalgebrasapplyclosed
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Lectures on bar and cobar

    math.AT 2025-07 conditional novelty 7.0 of 10

    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.

  2. Hochschild theory of multiplicative sequences of algebras and coalgebra measurings

    math.RA 2026-07 conditional novelty 6.0 of 10

    A new Hochschild theory is defined for multiplicative sequences of algebras, and coalgebra measurings between such sequences induce compatible maps on it.

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