{"paper":{"title":"A Compositional Framework for Bond Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Brandon Coya","submitted_at":"2017-09-29T21:27:24Z","abstract_excerpt":"Electrical circuits made only of perfectly conductive wires can be seen as partitions between finite sets. These are also known as \"corelations\" and are the morphisms in the category $\\mathrm{FinCorel}$. The two-element set has two different Frobenius monoid structures in $\\mathrm{FinCorel}$. These two Frobenius monoids are related to \"series\" and \"parallel\" junctions, which are used to connect pairs of wires. We show that these Frobenius monoids interact to form a \"weak bimonoid\" as defined by Pastro and Street. We conjecture a presentation for the subcategory of $\\mathrm{FinCorel}$ generated"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00098","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"}