{"paper":{"title":"Asymptotic Filtered Colimits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Kevin Sinclair, Logan Higginbotham","submitted_at":"2019-07-23T16:57:37Z","abstract_excerpt":"If one has a collection of large scale spaces $\\{(X_s,\\mathcal{LSS}_s)\\}_{s\\in S}$ with certain compatibility conditions one may define a large scale space on $X=\\bigcup\\limits_{s\\in S}X_s$ in a way where every function on $X$ is large scale continuous if and only if the function restricted to every $X_s$ is large scale continuous. This large scale structure is called the asymptotic filtered colimit of $\\{(X_s,\\mathcal{LSS}_s)\\}_{s\\in S}$. In this paper, we explore a wide variety of coarse invariants that are preserved between $\\{(X_s,\\mathcal{LSS}_s)\\}_{s\\in S}$ and the asymptotic filtered co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.10005","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"}