It is also true that the category of covering morphisms of a given groupoid B is equivalent to the category of actions of the groupoid B on sets.
32.
It is also true that the category of covering morphisms of a given groupoid B is equivalent to the category of actions of the groupoid B on sets.
33.
The groupoid \ mathcal I also allows for groupoids a notion of homotopy : it is a " unitinterval object " in the category of groupoids.
34.
The symmetries of the fifteen puzzle form a groupoid ( not a group, as not all moves can be composed ); this groupoid acts on configurations.
35.
The symmetries of the fifteen puzzle form a groupoid ( not a group, as not all moves can be composed ); this groupoid acts on configurations.
36.
This leads to the idea of modding out the gauge group to obtain the gauge groupoid as the closest description of the gauge connection in quantum field theory.
37.
The benefit in defining the fundamental groupoid of a graph of groups, as shown by, is that it is defined independently of base point or tree.
38.
Together with Martin Hofmann he received the 2014 LICS Test-of-Time Award for the paper " The groupoid model refutes uniqueness of identity proofs ".
39.
In category-theoretic terms, each connected component of a groupoid is isomorphic ) to a groupoid with a single object, that is, a single group.
40.
In category-theoretic terms, each connected component of a groupoid is isomorphic ) to a groupoid with a single object, that is, a single group.
