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

Andr\'e Joyal; Matthieu Anel

arxiv: 1309.6952 · v1 · pith:2XSXOKZLnew · submitted 2013-09-26 · 🧮 math.CT · math.AT· math.RA

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

Matthieu Anel , Andr\'e Joyal This is my paper

classification 🧮 math.CT math.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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Sweedler Theory for (co)algebras and the bar-cobar constructions

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