Circuit algebras are wheeled props

Z Dancso, I Halacheva, M Robertson - Journal of Pure and Applied Algebra, 2021 - Elsevier
Journal of Pure and Applied Algebra, 2021Elsevier
Circuit algebras, introduced by Bar-Natan and the first author, are a generalization of
Jones's planar algebras, in which one drops the planarity condition on “connection
diagrams”. They provide a useful language for the study of virtual and welded tangles in low-
dimensional topology. In this note, we present the circuit algebra analogue of the well-
known classification of planar algebras as pivotal categories with a self-dual generator. Our
main theorem is that there is an equivalence of categories between circuit algebras and the …
Abstract
Circuit algebras, introduced by Bar-Natan and the first author, are a generalization of Jones's planar algebras, in which one drops the planarity condition on “connection diagrams”. They provide a useful language for the study of virtual and welded tangles in low-dimensional topology. In this note, we present the circuit algebra analogue of the well-known classification of planar algebras as pivotal categories with a self-dual generator. Our main theorem is that there is an equivalence of categories between circuit algebras and the category of linear wheeled props – a type of strict symmetric tensor category with duals that arises in homotopy theory, deformation theory and the Batalin-Vilkovisky quantization formalism.
Elsevier
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