  Applications of category theory often involve symmetric monoidal categories
(SMCs), in which abstract processes or operations can be composed in series and
parallel. However, in 2020 there remains a dearth of computational tools for
working with SMCs. We present an "unbiased" approach to implementing symmetric
monoidal categories, based on an operad of directed, acyclic wiring diagrams.
Because the interchange law and other laws of a SMC hold identically in a
wiring diagram, no rewrite rules are needed to compare diagrams. We discuss the
mathematics of the operad of wiring diagrams, as well as its implementation in
the software package Catlab.
