Is the Tensor Product Associative?

[huyichen]

It is a well fact that tensor product is associative up to isomorphism, but how should I use Universal property(you know, diagrams that commute) to show that it is true?

 

[mathwonk]

http://www.math.uga.edu/%7Eroy/845-3.pdf

especially page 31

 

[Landau]

Show that both (U\otimes V)\otimes W and U\otimes (V\otimes W) both satisfy the universal property. By general nonsense they are then isomorphisc.