PlanetPhysics/Category of Representations

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