A 2-adjunction between representations and preorder morphisms
Abstract
The recently introduced model of representations has been defined and motivated somewhat ex-nihilo. In this document, I will show that representations are related to a more ''classical'' model through a 2-adjunction. The target model is that of preorder morphisms, i.e. maps between sets equipped with reflexive and transitive relation that satisfy some natural preservation property. The aim of this is two-fold: first, this provides in my opinion a further justification of representations, as an object in non-trivial yet tight connection to some natural constructs; and secondly it suggests some classical results about order preserving maps could have interesting consequences for representations. This work has been presented (but not published or peer-reviewed) at RAMiCS 2026.
Cite
@article{arxiv.2604.17942,
title = {A 2-adjunction between representations and preorder morphisms},
author = {Paul Brunet},
journal= {arXiv preprint arXiv:2604.17942},
year = {2026}
}