2021/08/10 by Sophie Raynor, Raynor, Sophie
Mathematics · #18M85 (Primary) 18M10 #57K12 (Secondary) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2108.04557
openalex publication_date 2021/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Circuit algebras, used in the study of finite-type knot invariants, are a symmetric analogue of Jones's planar algebras. They are very closely related to circuit operads, which are a variation of modular operads admitting an extra monoidal product. This paper gives a description of circuit algebras in terms categories of Brauer diagrams. An abstract nerve theorem for circuit operads -- and hence circuit algebras -- is proved using an iterated distributive law, and an existing nerve theorem for modular operads.