category of representations

Definition 0.1.

The categoryMathworldPlanetmath Rep(G) of representations has objects the representations of a groupoidPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath 𝖦, and as morphisms the intertwiners i:ρjρk that are (vector) bundle morphisms i:EE over the manifold M so that ρk(g)i=iρj. Because representations are functorsMathworldPlanetmath ρ:𝖦𝐕𝐞𝐜𝐭, an itertwiner i is in fact a natural transformation between two such functors that are groupoid representationsPlanetmathPlanetmathPlanetmathPlanetmath of 𝖦, in this case implemented via the vector bundleMathworldPlanetmath morphisms i:EE.

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