ABSTRACT

The main result of this chapter proves that the lifted Grothendieck construction is a non-symmetric Cat-multiequivalence. This proof uses the local characterization for adjoint Cat-multiequivalences. In other words, instead of explicitly constructing an adjoint inverse of the Grothendieck construction, this chapter shows that the Grothendieck construction is essentially surjective on objects and an isomorphism on each multimorphism category. This concludes Part II.