In any context it is of interest to ask which kind of morphisms arise as pullbacks along a classifying morphism to some universal object of some universal morphism The Grothendieck construction describes this in the context of Cat: a morphism of categories – i.e. a functor – is called a fibered category or Grothendieck fibration if it is encoded in a pseudofunctor/2-functor . The reconstruction of from the pseudofunctor is the Grothendieck construction which is a fully faithful 2-functor from...