Planar diagrammatics of self-adjoint functors and recognizable tree series
arXiv:2104.01417 · doi:10.4310/PAMQ.2023.v19.n5.a4
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.
arXiv comment61 pages. v2: This revised version is to appear in Pure Appl. Math. Q
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