{"paper":{"title":"Fibers of partial totalizations of a pointed cosimplicial space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Akhil Mathew, Vesna Stojanoska","submitted_at":"2014-08-07T17:41:16Z","abstract_excerpt":"Let $X^\\bullet$ be a cosimplicial object in a pointed $\\infty$-category. We show that the fiber of $\\mathrm{Tot}_m(X^\\bullet) \\to \\mathrm{Tot}_n(X^\\bullet)$ depends only on the pointed cosimplicial object $\\Omega^k X^\\bullet$ and is in particular a $k$-fold loop object, where $k = 2n - m+2$. The approach is explicit obstruction theory with quasicategories. We also discuss generalizations to other types of homotopy limits and colimits."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1665","kind":"arxiv","version":3},"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"}