A skew-duoidal Eckmann-Hilton argument and quantum categories
Category Theory
2014-11-10 v2
Abstract
A general result relating skew monoidal structures and monads is proved. This is applied to quantum categories and bialgebroids. Ordinary categories are monads in the bicategory whose morphisms are spans between sets. Quantum categories were originally defined as monoidal comonads on endomorphism objects in a particular monoidal bicategory M. Then they were shown also to be skew monoidal structures (with an appropriate unit) on objects in M. Now we see in what kind of M quantum categories are merely monads.
Cite
@article{arxiv.1210.8192,
title = {A skew-duoidal Eckmann-Hilton argument and quantum categories},
author = {Stephen Lack and Ross Street},
journal= {arXiv preprint arXiv:1210.8192},
year = {2014}
}
Comments
14 pages, dedicated to George Janelidze on the occasion of his 60th birthday; v2 final version, 15 pages, to appear in Applied Categorical Structures