Lemma
Let U and V be vector spaces, and let
b:UxV-->X be a bilinear map from UxV to a vector
space X. Suppose that for every bilinear map f
defined on UxV there is a unique linear map c
defined on X such that f=cb. Then there is an
isomorphism i:X-->U@V such that u@v=ib(u,v) for
every (u,v) in U@V.
We can avoid mentioning u@v if we use the map g:UxV-->U@V.
Then the lemma says that g=ib. Briefly, the point of the lemma is
that any bilinear map b:UxV-->X satisfying the universal property
is isomorphic to the map g:UxV-->U@V in an obvious sense.
