The Wehrheim–Woodward Category of Linear Canonical Relations between $G$-Spaces

We extend the work in a previous paper with David Li-Bland to construct the Wehrheim–Woodward category $\mathrm{WW}(G\mathbf{SLREL})$ of equivariant linear canonical relations between linear symplectic $G$-spaces for a compact group $G$. When $G$ is the trivial group, this reduces to the previous result that the morphisms in $\mathrm{WW}(\mathbf{SLREL})$ may be identified with pairs $(L,k)$ consisting of a linear canonical relation and a nonnegative integer.