Representations of multicategories of planar diagrams and tensor categories

Abstract

We shall discuss how the notions of multicategories and their linear representations are related with tensor categories. When one focuses on the ones arizing from planar diagrams, it particularly implies that there is a natural one-to-one correspondence between planar algebras and singly generated bicategories.

17 pages, based on conference talks at Indiana Univ.(2009) and RIMS(2010)

References in corpus (3)

• A categorical and diagrammatical approach to Temperley-Lieb algebras
• Fiber Functors on Temperley-Lieb Categories
• Oriented Kauffman diagrams and universal quantum groups