\newcommand{\sqdiagram}[9]{Failed to parse (unknown function "\diagram"): {\displaystyle \diagram #1 \rto^{#2} \dto_{#4}& \eqno{\mbox{#9}}} }

The \htmladdnormallink{category {http://planetphysics.us/encyclopedia/Cod.html} Failed to parse (unknown function "\grp"): {\displaystyle Rep(\grp)}


 of representations} has objects the representations of a groupoid Failed to parse (unknown function "\grp"): {\displaystyle \grp}


, and as morphisms the intertwiners  ${\displaystyle i:\rho _{j}\longrightarrow \rho _{k}}$ that are (vector) bundle morphisms ${\displaystyle i:E\longrightarrow E}$ over the manifold ${\displaystyle M}$ so that ${\displaystyle \rho _{k}(g)\circ i=i\circ \rho _{j}}$. Because representations are functors Failed to parse (unknown function "\grp"): {\displaystyle \rho: \grp \longrightarrow {\mathbf Vect}}


, an itertwiner ${\displaystyle i}$ is in fact a natural transformation between two such functors that are groupoid representations of Failed to parse (unknown function "\grp"): {\displaystyle \grp}


, in this case implemented {\it via} the vector bundle morphisms ${\displaystyle i:E\longrightarrow E}$.