Corpus ID: 118505122

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

@article{Anel2013SweedlerTF,
  title={Sweedler Theory for (co)algebras and the bar-cobar constructions},
  author={M. Anel and A. Joyal},
  journal={arXiv: Category Theory},
  year={2013}
}
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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