{"paper":{"title":"On the fibrewise effective Burnside $\\infty$-category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Clark Barwick, Saul Glasman","submitted_at":"2016-07-10T21:29:39Z","abstract_excerpt":"Effective Burnside $\\infty$-categories are the centerpiece of the $\\infty$-categorical approach to equivariant stable homotopy theory. In this \\'etude, we recall the construction of the twisted arrow $\\infty$-category, and we give a new proof that it is an $\\infty$-category, using an extremely helpful modification of an argument due to Joyal--Tierney. The twisted arrow $\\infty$-category is in turn used to construct the effective Burnside $\\infty$-category. We employ a variation on this theme to construct a fibrewise effective Burnside $\\infty$-category. To show that this constuctionworks fibre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02786","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"}