2-groupoid
Definition 0.1.
A 2-groupoid is a 2-category whose morphisms are all invertible, that is, ones such that, each -arrow (morphism) is invertible with respect to the morphism composition.
Remark 0.1.
An important reason for studying –categories, and especially -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 |