A presheaf C of categories consists of the following data: 1. For every local homeomorphism f:Y->X of topological spaces X, Y, a category C(f:Y->X); 2. For every diagram f°g:Z->Y->X of local homeomorphisms, a functor g^(-1) :C(f:Y->X)->C(f°g:Z->X); 3. For every diagram f°g°h:W->Z->Y->X of local homeomorphisms, an invertible natural transformation θ_(g, h) :h^(-1) g^(-1)->(g h)^(-1).
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