PlanetPhysics/Category of Representations

\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 [[../CategoricalGroupRepresentation/|representations]]} has [[../TrivialGroupoid/|objects]] the representations of a [[../GroupoidHomomorphism2/|groupoid]] Failed to parse (unknown function "\grp"): {\displaystyle \grp}
, and as [[../TrivialGroupoid/|morphisms]] the intertwiners  $i:{\rho }_j⟶{\rho }_k$ that are ([[../Vectors/|vector]]) bundle morphisms $i:E⟶E$ over the [[../NoncommutativeGeometry4/|manifold]] $M$ so that ${\rho }_k(g)\circ i=i\circ {\rho }_j$. Because representations are [[../TrivialGroupoid/|functors]] Failed to parse (unknown function "\grp"): {\displaystyle \rho: \grp \longrightarrow {\mathbf Vect}}
, an itertwiner $i$ is in fact a [[../VariableCategory2/|natural transformation]] between two such functors that are [[../GroupoidRepresentations/|groupoid representations]] of Failed to parse (unknown function "\grp"): {\displaystyle \grp}
, in this case implemented {\it via} the vector bundle morphisms $i:E⟶E$.