Circuit algebras are wheeled props
Abstract
Circuit algebras, introduced by BarNatan 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 lowdimensional topology. In this note, we present the circuit algebra analogue of the wellknown classification of planar algebras as pivotal categories with a selfdual 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 BatalinVilkovisky quantization formalism.
 Publication:

arXiv eprints
 Pub Date:
 September 2020
 arXiv:
 arXiv:2009.09738
 Bibcode:
 2020arXiv200909738D
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Algebraic Topology;
 57M25;
 18D50
 EPrint:
 29 pages, many figures