We can expect the coarse quotient to be a smooth manifold if for example the stabilizer groups are trivial ( as in the example of the ech groupoid ).
42.
The collapse of a groupoid into a mere collection of groups loses some information, even from a category-theoretic point of view, because it is not natural.
43.
So like " S " 1, the result follows from the groupoid Seifert-van Kampen Theorem, as in the book " Topology and Groupoids ".
44.
The Mathieu groupoid is a groupoid introduced by John Horton Conway acting on 13 points such that the elements fixing a point form a copy of the Mathieu group M 12.
45.
The Mathieu groupoid is a groupoid introduced by John Horton Conway acting on 13 points such that the elements fixing a point form a copy of the Mathieu group M 12.
46.
This occurs in topology because if a group acts on a space it also acts on the fundamental groupoid ( " X " ) } } of the space.
47.
A groupoid G has a universal group U ( G ) and the universal group of a disjoint union of groups is the free ( = coproduct ) of the groups.
48.
Applications of the fundamental groupoid on a set of base points to the Jordan curve theorem, covering spaces, and orbit spaces are given in Ronald Brown's book.
49.
A groupoid is an algebraic structure ( G, \ ast ) consisting of a non-empty set G and a binary partial function'\ ast'defined on G.
50.
Between the category of covering spaces of a reasonably nice space " X " and the category of groupoid covering morphisms of ? 1 ( " X " ).
