ABSTRACT
Part III is about the pseudo symmetric Cat-multifunctoriality of inverse K-theory P and its ramification in terms of preservation of pseudo symmetric algebraic structures. Inverse K-theory P involves two constructions: a functor A and a Grothendieck construction. This chapter discusses the first construction A. For the domain of inverse K-theory and A, this chapter first discusses the symmetric monoidal closed category of Γ-categories and its Cat-multicategory structure. Then it discusses the underlying functor of A and its extension to a Cat-multifunctor.
