Abstract
AbstractWe apply the theory of weighted bicategorical colimits to study the problem of existence and computation of such colimits of birepresentations of finitary bicategories. The main application of our results is the complete classification of simple transitive birepresentations of a bicategory studied previously by Zimmermann. The classification confirms a conjecture he has made.
Funder
Göran Gustafssons Stiftelse för Naturvetenskaplig och Medicinsk Forskning
Publisher
Springer Science and Business Media LLC
Subject
General Computer Science,Theoretical Computer Science,Algebra and Number Theory
Reference38 articles.
1. Brandenburg, M.: Bicategorical colimits of tensor categories. Preprint, arXiv:2001.10123
2. Canevali, N.: $$2$$-filtered bicolimits and finite weighted bilimits commute in Cat. Bachelor’s thesis, Universidad de Buenos Aires (2016)
3. Chan, A., Mazorchuk, V.: Diagrams and discrete extensions for finitary 2-representations. Math. Proc. Camb. Philos. Soc. 166(2), 325–352 (2019)
4. Chuang, J., Rouquier, R.: Derived equivalences for symmetric groups and sl$$_{2}$$-categorification. Ann. Math. (2) 167(1), 245–298 (2008)
5. Comes, J., Wilson, B.: Deligne’s category $$ {\text{ Rep }}(GL_{\delta })$$ and representations of general linear supergroups. Represent. Theory 16, 568–609 (2012)