$(X \times Y) \times Z = \lbrace \langle\langle x, y\rangle, z\rangle : x \in X, y \in Y, z\in Z \rbrace$

$X \times (Y \times Z) = \lbrace \langle x, \langle y, z\rangle\rangle : x \in X, y \in Y, z\in Z \rbrace$

$\alpha_{X, Y, Z} : \langle\langle x, y\rangle, z\rangle \mapsto \langle x, \langle y, z\rangle\rangle$

On a related note, is there a rigorous definition of "canonical"? I'd always assumed the term to be (mildly) informal.