Circuit algebras are wheeled props

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