  We show there exists a rigid monoidal category formed out by quantum linear
spaces with an additional structure, such that FRT bialgebras and corresponding
rectangular generalizations are its internal coEnd and coHom objects,
respectively. This enable us to think of them as the coordinate rings of a
quantum space of homomorphisms that preserve the mentioned structure. The well
known epimorphisms between FRT bialgebras and quantum semigroups (defined by
Manin) translate into `inclusions' of quantum spaces, as the space of
endomorphisms of a metric linear space V is included in gl(V). Our study is
developed for conic quantum spaces.
