Geodesic
The Wehrheim–Woodward Category of Linear Canonical Relations between $G$-Spaces
Symmetry, integrability and geometry: methods and applications, Tome 20 (2024)

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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.
Keywords: symplectic vector space, canonical relation, rigid monoidal category, highly selective category. 
Alan Weinstein. The Wehrheim–Woodward Category of Linear Canonical Relations between $G$-Spaces. Symmetry, integrability and geometry: methods and applications, Tome 20 (2024). http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a100/
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     author = {Alan Weinstein},
     title = {The {Wehrheim{\textendash}Woodward} {Category} of {Linear} {Canonical} {Relations} between $G${-Spaces}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a100/}
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