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