  This second part comes to the construction of the spectrum associated to a
situation of multi-adjunction. Exploiting a geometric understanding of its
multi-versal property, the spectrum of an object is obtained as the spaces of
local units equipped with a topology provided by orthogonality aspects. After
recalling Diers original construction, this paper introduces new material.
First we explain how the situation of multi-adjunction can be corrected in a
situation of adjunction between categories of modeled spaces as in the
topos-theoretic approach. Then we come to the 2-functorial aspects of the
process relatively to a 2-category of Diers contexts. We propose an
axiomatization of the notion of spectral duality through morphisms between
fibrations over a category of spatial objects, and show how such situations get
back right multi-adjoint functors.
