Mikhail Khovanov
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 |
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Biadjoint Functors And Trees - Final Manuscript
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