FRT Construction and Equipped Quantum Linear Spaces

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.