{"paper":{"title":"Proto-exact categories of matroids, Hall algebras, and K-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CO","math.RT"],"primary_cat":"math.CT","authors_text":"Christopher Eppolito, Jaiung Jun, Matt Szczesny","submitted_at":"2018-05-06T21:47:42Z","abstract_excerpt":"This paper examines the category $\\mathbf{Mat}_{\\bullet}$ of pointed matroids and strong maps from the point of view of Hall algebras. We show that $\\mathbf{Mat}_{\\bullet}$ has the structure of a finitary proto-exact category - a non-additive generalization of exact category due to Dyckerhoff-Kapranov. We define the algebraic K-theory $K_* (\\mathbf{Mat}_{\\bullet})$ of $\\mathbf{Mat}_{\\bullet}$ via the Waldhausen construction, and show that it is non-trivial, by exhibiting injections $$\\pi^s_n (\\mathbb{S}) \\hookrightarrow K_n (\\mathbf{Mat}_{\\bullet})$$ from the stable homotopy groups of spheres "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02281","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"}