A 2-adjunction between representations and preorder morphisms

technical report, 2026

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.

@unpublished{b26b,
    title = "A 2-adjunction between representations and preorder morphisms",
    author = "{Paul Brunet}",
    year = 2026,
    doi = "10.48550/arXiv.2604.17942"
}

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	Preprint on arXiv

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