PreprintCC BY-SA 4.0arXiv
Duality theory for categorical theories
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.
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BibTeX
@misc{ye2026duality,
title = {{Duality theory for categorical theories}},
author = {Lingyuan Ye},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.22071},
eprint = {2605.22071},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.22071},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Duality theory for categorical theories
AU - Lingyuan Ye
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2605.22071
UR - https://arxiv.org/abs/2605.22071
AB - 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.
ER -