Colimits of internal categories
Category Theory
2025-11-07 v4
Abstract
We show that for an extensive -category with pullbacks and pullback stable coequalisers in which the forgetful functor has left adjoint, the -category of internal categories, functors and natural transformations has finite -colimits. In addition, is extensive, has pullbacks and codescent coequalisers are stable under pullback along discrete Conduch\'{e} fibrations. Moreover, we give converse results to this.
Cite
@article{arxiv.2501.17769,
title = {Colimits of internal categories},
author = {Calum Hughes and Adrian Miranda},
journal= {arXiv preprint arXiv:2501.17769},
year = {2025}
}
Comments
29 pages, comments welcome. V4, added important reference and alternative proof