{"paper":{"title":"Categories of Pseudocones and Equivariant Descent","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT","math.CT"],"primary_cat":"math.AG","authors_text":"Geoff Vooys","submitted_at":"2024-01-18T18:01:57Z","abstract_excerpt":"In this monograph we provide an in-depth and systematic study of pseudolimits of pseudofunctors $F:\\mathscr{C}^{op} \\to \\mathfrak{Cat}$ in the $2$-category of categories where $\\mathscr{C}$ is a $1$-category and use this to give an explicit and careful study of the category theory used in representation theory, equivariant algebraic geometry, and equivariant algebraic topology and give a unifying language to study equivariant sheaves, equivariant perverse sheaves, and their equivariant derived categories. We show how to use the pseudocone construction $\\mathsf{Bicat}(\\mathscr{C}^{op},\\mathfrak"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.10172","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.10172/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}