Duality theory for categorical theories
Category Theory
2026-05-22 v1 Logic
Abstract
We have generalised the notion of categorical theory in model theory to the context of coherent theories. We prove a duality result between the full sub-2-category of pretopoi which are categorical, and the 2-category of profinite monoids. We also study the geometry of profinite monoids via the classifying topos construction, and show it identifies them as a full sub-2-category of the 2-category of topoi.
Cite
@article{arxiv.2605.22071,
title = {Duality theory for categorical theories},
author = {Lingyuan Ye},
journal= {arXiv preprint arXiv:2605.22071},
year = {2026}
}