  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.
