Finitary birepresentations of finitary bicategories
| Autor: | Vanessa Miemietz, Marco Mackaay, Daniel Tubbenhauer, Volodymyr Mazorchuk, Xiaoting Zhang |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Reduction (recursion theory) Generalization General Mathematics Coalgebra 01 natural sciences Simple (abstract algebra) Computer Science::Logic in Computer Science Mathematics::Category Theory 0103 physical sciences FOS: Mathematics Finitary Category Theory (math.CT) 0101 mathematics Representation Theory (math.RT) Mathematics Transitive relation Applied Mathematics 010102 general mathematics Mathematics - Category Theory 16. Peace & justice Mathematics::Logic Double centralizer theorem 010307 mathematical physics Bijection injection and surjection Mathematics - Representation Theory |
| Popis: | In this paper, we discuss the generalization of finitary $2$-representation theory of finitary $2$-categories to finitary birepresentation theory of finitary bicategories. In previous papers on the subject, the classification of simple transitive $2$-representations of a given $2$-category was reduced to that for certain subquotients. These reduction results were all formulated as bijections between equivalence classes of $2$-representations. In this paper, we generalize them to biequivalences between certain $2$-categories of birepresentations. Furthermore, we prove an analog of the double centralizer theorem in finitary birepresentation theory. Significant revision of the original version |
| Databáze: | OpenAIRE |
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