# category of representations

###### Definition 0.1.

The *category ^{} $R\mathit{}e\mathit{}p\mathit{}\mathrm{(}\mathrm{G}\mathrm{)}$ of representations* has objects the representations of a groupoid

^{}$\U0001d5a6$, and as morphisms the

*intertwiners*$i:{\rho}_{j}\u27f6{\rho}_{k}$ that are (vector) bundle morphisms $i:E\u27f6E$ over the manifold $M$ so that ${\rho}_{k}(g)\circ i=i\circ {\rho}_{j}$. Because representations are functors

^{}$\rho :\U0001d5a6\u27f6\mathrm{\mathbf{V}\mathbf{e}\mathbf{c}\mathbf{t}}$, an itertwiner $i$ is in fact a natural transformation between two such functors that are groupoid representations

^{}of $\U0001d5a6$, in this case implemented via the vector bundle

^{}morphisms $i:E\u27f6E$.

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 |