{"paper":{"title":"A theory of 2-pro-objects (with expanded proofs)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Eduardo J. Dubuc, M. Emilia Descotte","submitted_at":"2014-06-22T21:05:21Z","abstract_excerpt":"Grothendieck develops the theory of pro-objects over a category $\\mathsf{C}$. The fundamental property of the category $\\mathsf{Pro}(\\mathsf{C})$ is that there is an embedding $\\mathsf{C} \\overset{c}{\\longrightarrow} \\mathsf{Pro}(\\mathsf{C})$, the category $\\mathsf{Pro}(\\mathsf{C})$ is closed under small cofiltered limits, and these limits are free in the sense that for any category $\\mathsf{E}$ closed under small cofiltered limits, pre-composition with $c$ determines an equivalence of categories $\\mathcal{C}at(\\mathsf{Pro}(\\mathsf{C}),\\,\\mathsf{E})_+ \\simeq \\mathcal{C}at(\\mathsf{C},\\, \\mathsf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5762","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"}