# Borel morphism

###### Definition 0.1.

Let ${\mathbb{G}}_{B}$ and ${\mathbb{G}}_{B}$* be two groupoids^{} whose object spaces are Borel. An *algebraic morphism* from ${\mathbb{G}}_{B}$
to ${\mathbb{G}}_{B}$* is defined as a left action of ${\mathbb{G}}_{B}$ on ${\mathbb{G}}_{B}$* which commutes with the multiplication on ${\mathbb{G}}_{B}$. Such an algebraic morphism between Borel groupoids is said to be a *Borel morphism* if the action of ${\mathbb{G}}_{B}$ on ${\mathbb{G}}_{B}$* is Borel (viz. ref. [1])

## References

- 1 M.R. Buneci. 2006., http://www.utgjiu.ro/math/mbuneci/preprint/p0024.pdfGroupoid C*-Algebras., Surveys in Mathematics and its Applications, Volume 1: 71–98.

Title | Borel morphism |

Canonical name | BorelMorphism |

Date of creation | 2013-03-22 18:23:36 |

Last modified on | 2013-03-22 18:23:36 |

Owner | bci1 (20947) |

Last modified by | bci1 (20947) |

Numerical id | 12 |

Author | bci1 (20947) |

Entry type | Definition |

Classification | msc 60A10 |

Classification | msc 28A12 |

Classification | msc 28C15 |

Classification | msc 54H05 |

Classification | msc 28A05 |

Related topic | BorelSpace |

Related topic | Groupoids |

Related topic | CategoryOfBorelSpaces |

Related topic | MeasurableFunctions |

Related topic | BorelMeasure |

Defines | algebraic morphism |