# category of representations

###### Definition 0.1.

The category $Rep({\mathsf{G}})$ of representations has objects the representations of a groupoid ${\mathsf{G}}$, 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 $\rho:{\mathsf{G}}\longrightarrow{\bf Vect}$, an itertwiner $i$ is in fact a natural transformation between two such functors that are groupoid representations of ${\mathsf{G}}$, in this case implemented via the vector bundle morphisms $i:E\longrightarrow E$.

 Title category of representations Canonical name CategoryOfRepresentations Date of creation 2013-03-22 19:19:26 Last modified on 2013-03-22 19:19:26 Owner bci1 (20947) Last modified by bci1 (20947) Numerical id 8 Author bci1 (20947) Entry type Definition Classification msc 22A22 Classification msc 20L05 Related topic GroupoidRepresentation4 Related topic RepresentationsOfLocallyCompactGroupoids Related topic Functor Defines morphisms of representations Defines representation morphism