{"paper":{"title":"The homomorphism lattice induced by a finite algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Brian A. Davey, Charles T. Gray, Jane G. Pitkethly","submitted_at":"2016-03-01T03:50:03Z","abstract_excerpt":"Each finite algebra $\\mathbf A$ induces a lattice~$\\mathbf L_{\\mathbf A}$ via the quasi-order~$\\to$ on the finite members of the variety generated by~$\\mathbf A$, where $\\mathbf B \\to \\mathbf C$ if there exists a homomorphism from $\\mathbf B$ to~$\\mathbf C$. In this paper, we introduce the question: `Which lattices arise as the homomorphism lattice $\\mathbf L_{\\mathbf A}$ induced by a finite algebra $\\mathbf A$?' Our main result is that each finite distributive lattice arises as~$\\mathbf L_{\\mathbf Q}$, for some quasi-primal algebra~$\\mathbf Q$. We also obtain representations of some other cla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00129","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"}