{"paper":{"title":"Verdier quotients of stable quasi-categories are localizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Brad Drew","submitted_at":"2015-11-26T04:12:20Z","abstract_excerpt":"The Verdier quotient $\\mathcal{T}/\\mathcal{S}$ of a triangulated category $\\mathcal{T}$ by a triangulated subcategory $\\mathcal{S}$ is defined by a universal property with respect to triangulated functors out of $\\mathcal{T}$. However, $\\mathcal{T}/\\mathcal{S}$ is in fact a localization of $\\mathcal{T}$, i.e., it is obtained from $\\mathcal{T}$ by formally inverting a class of morphisms. We establish the analogous result for small stable quasi-categories. As an application, we explore the compatibility of Verdier quotients with symmetric monoidal structures. In particular, we record a few usefu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08287","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"}