{"paper":{"title":"Topology from enrichment: the curious case of partial metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.CT","authors_text":"Dirk Hofmann, Isar Stubbe","submitted_at":"2016-07-08T08:29:16Z","abstract_excerpt":"For any small quantaloid $\\Q$, there is a new quantaloid $\\D(\\Q)$ of diagonals in $\\Q$. If $\\Q$ is divisible then so is $\\D(\\Q)$ (and vice versa), and then it is particularly interesting to compare categories enriched in $\\Q$ with categories enriched in $\\D(\\Q)$. Taking Lawvere's quantale of extended positive real numbers as base quantale, $\\Q$-categories are generalised metric spaces, and $\\D(\\Q)$-categories are generalised partial metric spaces, i.e.\\ metric spaces in which self-distance need not be zero and with a suitably modified triangular inequality. We show how every small quantaloid-e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02269","kind":"arxiv","version":2},"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"}