Presheaf of Categories

A presheaf of categories consists of the following data:

1. For every local homeomorphism of topological spaces , , a category ;

2. For every diagram of local homeomorphisms, a functor ;

3. For every diagram of local homeomorphisms, an invertible natural transformation .

In addition, for every diagram

of topological spaces , , , , and , commutativity is required in the above diagram.