A fibered category morphism 
between fibered
categories 
and 
over a topological space 
consists of:
1. a functor 
for each open subset 
and
2. a natural isomorphism 
for each inclusion 
.
It is required that these structures satisfy a compatibility condition with respect to the 
's,
namely, that for the inclusions 
, 
, the above diagram should commute.
