{"paper":{"title":"Categorical centers and Yetter--Drinfel`d-modules as 2-categorical (bi)lax structures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Bojana Femi\\'c, Sebastian Halbig","submitted_at":"2023-06-08T16:37:15Z","abstract_excerpt":"The bicategorical point of view provides a natural setting for many concepts in the representation theory of monoidal categories. We show that centers of twisted bimodule categories correspond to categories of 2-dimensional natural transformations and modifications between the deloopings of the twisting functors. We also show that dualities lift to centers of twisted bimodule categories. Inspired by the notion of (pre)bimonoidal functors due to McCurdy and Street and by bilax functors of Aguiar and Mahajan, we study 2-dimensional functors which are simultaneously lax and colax with a compatibi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.05337","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/2306.05337/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"}