{"paper":{"title":"Exit paths and constructible stacks","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"David Treumann","submitted_at":"2007-08-05T04:06:38Z","abstract_excerpt":"For a Whitney stratification S of a space X (or more generally a topological stratification in the sense of Goresky and MacPherson) we introduce the notion of an S-constructible stack of categories on X. The motivating example is the stack of S-constructible perverse sheaves. We introduce a 2-category $EP_{\\leq 2}(X,S)$, called the exit-path 2-category, which is a natural stratified version of the fundamental 2-groupoid. Our main result is that the 2-category of S-constructible stacks on X is equivalent to the 2-category of 2-functors from $EP_{\\leq 2}(X,S)$ to the 2-category of small categori"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.0659","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"}