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Pure and Applied Mathematics Quarterly
Volume 19 (2023)
Number 5
Special issue on “Subfactors and Related Topics” in memory of Vaughan Jones
Guest Editors: Dietmar Bisch, Arthur Jaffe, Yasuyuki Kawahigashi, and Zhengwei Liu
Planar diagrammatics of self-adjoint functors and recognizable tree series
Pages: 2409 – 2499
DOI: https://dx.doi.org/10.4310/PAMQ.2023.v19.n5.a4
Authors
Abstract
A pair of biadjoint functors between two categories produces a collection of elements in the centers of these categories, one for each isotopy class of nested circles in the plane. If the centers are equipped with a trace map into the ground field, then one assigns an element of that field to a diagram of nested circles. We focus on the self-adjoint functor case of this construction and study the reverse problem of recovering such a functor and a category given values associated to diagrams of nested circles.
Keywords
self-adjoint functor, universal construction, monoidal category, Temperley–Lieb category, recognizable tree series
M. K. was partially supported via NSF grant DMS-1807425.
R. L. was supported by a Nottingham Research Fellowship.
Received 5 April 2021
Received revised 6 October 2021
Accepted 30 October 2021
Published 30 January 2024