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

By M. Anel, André Joyal. 2013

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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.

View Paper: https://www.semanticscholar.org/paper/1b00488ffc092fa234cc8d586e18e3cc81b948d9