Simple transitive 2-representations via (co)algebra 1-morphisms
Representation Theory
2020-03-05 v4 Category Theory
Quantum Algebra
Abstract
For any fiat 2-category C, we show how its simple transitive 2-representations can be constructed using coalgebra 1-morphisms in the injective abelianization of C. Dually, we show that these can also be constructed using algebra 1-morphisms in the projective abelianization of C. We also extend Morita-Takeuchi theory to our setup and work out several examples explicitly.
Cite
@article{arxiv.1612.06325,
title = {Simple transitive 2-representations via (co)algebra 1-morphisms},
author = {Marco Mackaay and Volodymyr Mazorchuk and Vanessa Miemietz and Daniel Tubbenhauer},
journal= {arXiv preprint arXiv:1612.06325},
year = {2020}
}
Comments
Revised version to appear in Indiana Univ. Math. J. the numbering of theorems etc. is changed to adjust to the published version