On monads and warpings

Stephen Lack; Ross Street

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arXiv · 1408.4953

On monads and warpings

Stephen Lack·Ross Street

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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.

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Stephen Lack, Ross Street. 2014-08-21. On monads and warpings. https://arxiv.org/abs/1408.4953

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