On Structures in Arrow Categories
Category Theory
2023-09-28 v1
Abstract
In this article we investigate which categorical structures of a category C are inherited by its arrow category. In particular, we show that a monoidal equivalence between two categories gives rise to a monoidal equivalence between their arrow categories. Moreover, we examine under which circumstances an arrow category is rigid and pivotal. Finally, we derive what the (co)algebra, bialgebra and Hopf algebra objects are in an arrow category.
Cite
@article{arxiv.2309.15544,
title = {On Structures in Arrow Categories},
author = {Paulina L. A. Goedicke and Jamie Vicary},
journal= {arXiv preprint arXiv:2309.15544},
year = {2023}
}