  Adapting the idea of twisted tensor products to the category of finitely
generated algebras, we define on its opposite, the category QLS of quantum
linear spaces, a family of objects hom(B,A)^{op}, one for each pair
A^{op},B^{op} there, with analogous properties to its internal Hom ones, but
representing spaces of transformations whose coordinate rings hom(B,A) and the
ones of their respective domains B^{op} do not commute among themselves. The
mentioned non commutativity is controlled by a collection of twisting maps
\tau_{A,B}. We show that the (bi)algebras end(A)=hom(A,A), under certain
circumstances, are 2-cocycle twistings of the quantum semigroups end(A) in the
untwisted case. This fact generalizes the twist equivalence (at a semigroup
level) between, for instance, the quantum groups GL_{q}(n) and their
multiparametric versions GL_{q,\phi}(n).
