Planar diagrammatics of self-adjoint functors and recognizable tree series

Khovanov, Mikhail; Laugwitz, Robert

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.

• Journal Article Type: Article
• Acceptance Date: Oct 30, 2021
• Online Publication Date: Jan 30, 2024
• Publication Date: 2023
• Deposit Date: Nov 4, 2021
• Publicly Available Date: Dec 31, 2023
• Journal: Pure and Applied Mathematics Quarterly
• Print ISSN: 1558-8599
• Electronic ISSN: 1558-8602
• Publisher: International Press
• Peer Reviewed: Peer Reviewed
• Volume: 19
• Issue: 5
• Pages: 2409-2499
• DOI: https://doi.org/10.4310/pamq.2023.v19.n5.a4
• Keywords: self-adjoint functor, universal construction, monoidal category, Temperley–Lieb category, recognizable tree series
• Public URL: https://nottingham-repository.worktribe.com/output/6611067
• Publisher URL: https://www.intlpress.com/site/pub/pages/journals/items/pamq/content/vols/0019/0005/a004/index.php