{"paper":{"title":"The diagonal of a multicosimplicial object","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Philip S. Hirschhorn","submitted_at":"2015-06-23T01:42:36Z","abstract_excerpt":"We show that the functor that takes a multicosimplicial object in a model category to its diagonal cosimplicial object is a right Quillen functor. This implies that the diagonal of a Reedy fibrant multicosimplicial object is a Reedy fibrant cosimplicial object, which has applications to the calculus of functors. We also show that, although the diagonal functor is a Quillen functor, it is not a Quillen equivalence for multicosimplicial spaces.\n  We also discuss total objects and homotopy limits of multicosimplicial objects. We show that the total object of a multicosimplicial object is isomorph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06837","kind":"arxiv","version":4},"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"}