Skew-monoidal categories and bialgebroids

@article{Szlachnyi2012SkewmonoidalCA,
  title={Skew-monoidal categories and bialgebroids},
  author={K. Szlach{\'a}nyi},
  journal={Advances in Mathematics},
  year={2012},
  volume={231},
  pages={1694-1730}
}
Abstract Skew-monoidal categories arise when the associator and the left and right units of a monoidal category are, in a specific way, not invertible. We prove that the closed skew-monoidal structures on the category of right R -modules are precisely the right bialgebroids over the ring R . These skew-monoidal structures induce quotient skew-monoidal structures on the category of R – R -bimodules and this leads to the following generalization: Opmonoidal monads on a monoidal category… Expand
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