  In [1] we introduced the concept of structured space, which is a topological
space that locally resembles some algebraic structures. In [2] we proceeded the
study of these spaces, developing two cohomology theories. The aim of this
paper is to define categories of structured spaces, (pre)sheaves with values in
such categories, and generalised notions of vector bundles, ringed spaces and
schemes. Then, we will construct (using some techniques and also the general
method in Section 2 of [2]) various cohomology theories for these objects.
