@Michael – I think we can simplify your answer slightly:
\[ (X \times Y) \times Z = \lbrace \langle\langle x, y\rangle, z\rangle : x \in X, y \in Y, z\in Z \rbrace \]
\[ X \times (Y \times Z) = \lbrace \langle x, \langle y, z\rangle\rangle : x \in X, y \in Y, z\in Z \rbrace \]
\[ \alpha_{X, Y, Z} : \langle\langle x, y\rangle, z\rangle \mapsto \langle x, \langle y, z\rangle\rangle \]
On a related note, is there a rigorous definition of "canonical"? I'd always assumed the term to be (mildly) informal.
\[ (X \times Y) \times Z = \lbrace \langle\langle x, y\rangle, z\rangle : x \in X, y \in Y, z\in Z \rbrace \]
\[ X \times (Y \times Z) = \lbrace \langle x, \langle y, z\rangle\rangle : x \in X, y \in Y, z\in Z \rbrace \]
\[ \alpha_{X, Y, Z} : \langle\langle x, y\rangle, z\rangle \mapsto \langle x, \langle y, z\rangle\rangle \]
On a related note, is there a rigorous definition of "canonical"? I'd always assumed the term to be (mildly) informal.
Version 2.1.8p2
