{"paper":{"title":"An axiomatic construction of an almost full embedding of the category of graphs into the category of R-objects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CT"],"primary_cat":"math.RA","authors_text":"Adam J. Prze\\'zdziecki, R\\\"udiger G\\\"obel","submitted_at":"2013-05-15T13:16:39Z","abstract_excerpt":"We construct embeddings G of the category of graphs into categories of R-modules over a commutative ring R which are almost full in the sense that the maps induced by the functoriality of G\n  R[Hom_Graphs(X,Y)] --> Hom_R(GX,GY) are isomorphisms. The symbol R[S] above denotes the free R-module with the basis S. This implies that, for any cotorsion-free ring R, the categories of R-modules are not less complicated than the category of graphs. A similar embedding of graphs into the category of vector spaces with four distinguished subspaces (over any field, e.g. F_2={0,1} is obtained)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3458","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"}