Hi, just want to clear up something,
In class we saw an example of proving an isomorphism involving tensor algebras, something of the form . We used the universal property of tensor product, finding a bilinear map which give us map , then we tried to find an inverse map or just to prove that was surjective and one to one.
My question is, ¿Aren’t we forgetting to check that satisfies ? I mean, the universal property doesn’t yield an homomorphism of algebras at all. I understand that it’s just a linear map. ..