# 2-groupoid

###### Definition 0.1.

A 2-groupoid is a 2-category whose morphisms^{} are all invertible, that is, ones such that,
each $1$-arrow (morphism) is invertible with respect to the morphism composition.

###### Remark 0.1.

An important reason for studying $2$–categories, and especially $2$-groupoids, is to use them as coefficient objects for non-Abelian Cohomology theories. Thus, some double groupoids^{} defined over Hausdorff spaces that are non-Abelian^{} (or non-commutative) are relevant to non-Abelian Algebraic Topology (NAAT) and http://planetphysics.org/?op=getobj&from=lec&id=61NAQAT (or NA-QAT).

One needs to distinguish between a 2-groupoid and a double-groupoid as the two concepts are very different. Interestingly, some double groupoids defined over Hausdorff spaces that are non-Abelian (or non-commutative) have true two-dimensional geometric representations with special properties that allow generalizations^{} of important theorems in algebraic topology and higher dimensional algebra, such as the generalized van Kampen theorem^{} with significant consequences that cannot be obtained through Abelian^{} means.

Title | 2-groupoid |

Canonical name | 2groupoid |

Date of creation | 2013-03-22 19:21:09 |

Last modified on | 2013-03-22 19:21:09 |

Owner | bci1 (20947) |

Last modified by | bci1 (20947) |

Numerical id | 17 |

Author | bci1 (20947) |

Entry type | Definition |

Classification | msc 55Q35 |

Classification | msc 55Q05 |

Classification | msc 20L05 |

Classification | msc 18D05 |

Classification | msc 18-00 |

Synonym | 2-category with invertible morphisms |

Defines | 2-groupoid |

Defines | HDA |

Defines | higher dimensional algebra |

Defines | (m-1) arrows |

Defines |