{"paper":{"title":"On the unicity of formal category theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Fosco Loregian, Ivan Di Liberti","submitted_at":"2019-01-06T18:58:30Z","abstract_excerpt":"We prove an equivalence between cocomplete Yoneda structures and certain proarrow equipments on a 2-category $\\mathcal K$. In order to do this, we recognize the presheaf construction of a cocomplete Yoneda structure as a relative, lax idempotent monad sending each admissible 1-cell $f :A \\to B$ to an adjunction $\\boldsymbol{P}_!f\\dashv\\boldsymbol{P}^*f$. Each cocomplete Yoneda structure on $\\mathcal K$ arises in this way from a relative lax idempotent monad \"with enough adjoint 1-cells\", whose domain generates the ideal of admissibles, and the Kleisli category of such a monad equips its domain"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01594","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}