Scaled-free objects II

摘要

This work creates two categories of "array-weighted sets" for the purposes ofconstructing universal matrix-normed spaces and algebras. These universalobjects have the analogous universal property to the free vector space, liftingmaps completely bounded on a generation set to a completely bounded linear mapof the matrix-normed space. Moreover, the universal matrix-normed algebra is used to prove the existenceof a free product for matrix-normed algebras using algebraic methods.