On monads and warpings
arXiv:1408.4953
Abstract
We explain the sense in which a warping on a monoidal category is the same as a pseudomonad on the corresponding one-object bicategory, and we describe extensions of this to the setting of skew monoidal categories: these are a generalization of monoidal categories in which the associativity and unit maps are not required to be invertible. Our analysis leads us to describe a normalization process for skew monoidal categories, which produces a universal skew monoidal category for which the right unit map is invertible.
15 pages. Version 2: revised based on a very helpful report from the referee. To appear in the Cahiers de Topologie and Geometrie Differentielle Categoriques