Question about product of categories exercise I am stuck on a question because I do not understand what the question is asking.
I am reading Mac Lane's CTFWM (2nd ed.), on p.39, exercise 1 the question reads: 

Show that the product of categories includes the following known special cases: the product of monoids, of groups, of sets.

I do not understand what this means, or what I need to show. I understand exercise 2: show that the product of two preorders is a preorder. 
What is the difference between these two questions? Thanks.
 A: A group can be viewed as a one-object category in which every arrow is invertible as follows: given a group $G$, the object of the category $\mathbf{G}$ is a single element $\bullet$. There is one  arrow of $\mathbf{G}$ for each element of $G$, with composition of arrows corresponding to multiplication of elements. So the composing the arrow corresponding to $g$ with the arrow corresponding to $h$ is $hg$ (do $g$ first, then $h$). The identity arrow corresponds to the identity element of $G$. Conversely, any one-object category $\mathbf{C}$ in which every arrow is invertible corresponds to a group, with underlying set $\mathbf{C}(\bullet,\bullet)$, and multiplication of elements corresponding to composition of arrows.
Likewise, a monoid $M$ can be viewed as a one-object category in the same manner, and any one-object category can be viewed as a monoid (the underlying set being the set of arrows, and operation being composition).
Finally, a set $S$ can be viewed as a category where you have one object for every element of $S$, and the only arrows are the identity morphisms. And any category in which the only arrows are the identity morphisms corresponds to a set, namely the set of objects. 
Mac Lane has just finished defining the product of categories. The exercise asks you to show that if you have two groups $G$ and $H$, and view them as categories $\mathbf{G}$ and $\mathbf{H}$, then the product of the categories $\mathbf{G}$ and $\mathbf{H}$ will be a category that corresponds to the group $G\times H$. Likewise for monoids, and for sets. 
