Hom $\omega$-categories of a computad are free
Category Theory
2024-11-14 v3 Logic in Computer Science
Abstract
We provide a new description of the hom functor on weak -categories, and we show that it admits a left adjoint that we call the suspension functor. We then show that the hom functor preserves the property of being free on a computad, in contrast to the hom functor for strict -categories. Using the same technique, we define the opposite of an -category with respect to a set of dimensions, and we show that this construction also preserves the property of being free on a computad. Finally, we show that the constructions of opposites and homs commute.
Keywords
Cite
@article{arxiv.2402.01611,
title = {Hom $\omega$-categories of a computad are free},
author = {Thibaut Benjamin and Ioannis Markakis},
journal= {arXiv preprint arXiv:2402.01611},
year = {2024}
}
Comments
45 pages, updated to change the structure of the paper, add the suspension of $\omega$-categories, change the title and abstract accordingly, add citations and correct a few typos