{"paper":{"title":"A stratified homotopy hypothesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.GT"],"primary_cat":"math.AT","authors_text":"David Ayala, John Francis, Nick Rozenblyum","submitted_at":"2015-02-05T20:50:36Z","abstract_excerpt":"We show that conically smooth stratified spaces embed fully faithfully into $\\infty$-categories. This articulates a stratified generalization of the homotopy hypothesis proposed by Grothendieck. As such, each $\\infty$-category defines a stack on conically smooth stratified spaces, and we identify the descent conditions it satisfies. These include $\\mathbb{R}^1$-invariance and descent for open covers and blow-ups, analogous to sheaves for the h-topology in $\\mathbb{A}^1$-homotopy theory. In this way, we identify $\\infty$-categories as striation sheaves, which are those sheaves on conically smoo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01713","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"}