Tanning
The term Gerbe is used in algebraic topology for a specific type of stack over a topological space. Sometimes, however, special cases of such tanning are also referred to for simplicity as tanning, for example bundle tanning or Hitchin tanning . An important characterization of tanning is its bond.
Definition: A Gerbe over a topological space is a stack over in the 2 category of Gruppoids , which satisfies the following two Gerben axioms:
- There's an object in with .
- For every object in and two objects , in there is a morphism in and a morphism in .
The first axiom thus requires that it is non-trivial, while the second axiom represents a certain transitivity condition.