{"paper":{"title":"Fibrations and lax limits of $(\\infty,2)$-categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Andrea Gagna, Edoardo Lanari, Yonatan Harpaz","submitted_at":"2020-12-08T16:27:50Z","abstract_excerpt":"We study four types of (co)cartesian fibrations of $\\infty$-bicategories over a given base $\\mathcal{B}$, and prove that they encode the four variance flavors of $\\mathcal{B}$-indexed diagrams of $\\infty$-categories. We then use this machinery to set up a general theory of 2-(co)limits for diagrams valued in an $\\infty$-bicategory, capable of expressing lax, weighted and pseudo limits. When the $\\infty$-bicategory at hand arises from a model category tensored over marked simplicial sets, we show that this notion of 2-(co)limit can be calculated as a suitable form of a weighted homotopy limit o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.04537","kind":"arxiv","version":2},"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/2012.04537/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"}