The canonical kind of morphisms between multicategories are multifunctors. This generalized the concept of functor between categories and that of monoidal functors between monoidal categories.
The construction of K-theory spectra of permutative categories constitutes a multifunctor
between multicategories of permutative categories (under Deligne tensor product) and spectra (under smash product of spectra).
Hence for a multilinear functor of permutative categories
there is a compatibly induced morphism of K-spectra out of the smash product
This implies that the construction further extends to a 2-functor from the 2-category of enriched categories over the multicategory of permutative categories to that of enriched categories of spectra:
which applies to each hom-object.
(May 80, theorem 1.6, Theorem 2.1, Elmendorf-Mandell 04, theorem 1.1, Guillou 10, Theorem 1.1
See for instance
Created on September 16, 2018 at 04:11:55. See the history of this page for a list of all contributions to it.