Notational question: What is $Cat(-,-)$?

Question

(MacLane's Category theory) This is just simply a notational question so forgive me although it is relatively easy...

On page 44, there is a problem: For small category theory $A$,$B$ and $C$ establish a bijection $Cat(A\times B,C)\simeq Cat(A,B^C)$, and show it natural in $A$,$B$ and $C$.

My question is: What does $Cat(A\times B, C)$ mean?

Answer 1

It is $\mathcal{A}(A,B)$ the set of morphisms from $A$ to $B$ in the category $\mathcal{A}$. Also $\mathcal{A}(\_,\_)$ denotes the Hom-functor $\mathcal{A}^{\operatorname{op}} \times \mathcal{A} \to \mathsf{Set}$.

In your case you are talking about a set of functors.