I went to a lecture on category theory, and I am trying to understand something: I want to know what it means for a category to be distributive. We were given a homework problem, but I don't even understand what it means: Let $C$ be a category such that for all $X,Y \in C$ there exists a product $X \times Y$ and a coproduct $X \oplus Y$ in $C$. Show that there is a canonical morphism

$\psi : (X \times Y) \oplus (X \times Z) \to X \times (Y \oplus Z)$. When $\psi$ is an isomorphism, $C$ is called a {distributive category}.

What does "Show there is a canonical morphism $\psi : (X \times Y) \oplus (X \times Z) \to X \times (Y \oplus Z)$ mean? What does "canonical morphism" mean? By the way, functors have not yet been introduced in the course. So far we have only learned the definition of category, product, and coproduct.

The homework was already due, so I did not turn this in. At this point, I have no opportunity to turn something in, and I am just trying to understand.

ishomework. – David Roberts Sep 23 '11 at 2:26