A 2-adjunction between representations and preorder morphisms
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915945468919808 |
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| author | Brunet, Paul |
| author_facet | Brunet, Paul |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17942 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A 2-adjunction between representations and preorder morphisms Brunet, Paul Logic in Computer Science Category Theory 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. |
| title | A 2-adjunction between representations and preorder morphisms |
| topic | Logic in Computer Science Category Theory |
| url | https://arxiv.org/abs/2604.17942 |