English

On monads and warpings

Category Theory 2016-05-24 v2

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.

Keywords

Cite

@article{arxiv.1408.4953,
  title  = {On monads and warpings},
  author = {Stephen Lack and Ross Street},
  journal= {arXiv preprint arXiv:1408.4953},
  year   = {2016}
}

Comments

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

R2 v1 2026-06-22T05:35:28.802Z