natural numbers multiplication and category theory product Are the multiplication and summation on natural numbers kind of product and coproduct in category theory? and if yes then how?
 A: Yes, the categorical product and coproduct correspond to multiplication and addition in a fairly intuitive way.
Suppose we work in the category $\mathcal C$ of finite sets. For each finite set $X$, we of course have a number $|X|$, which is its cardinality. Taking the cardinality corresponds to counting the objects of $X$.
The coproduct $X \sqcup Y$ is simply a disjoint union. We have the relation
$$|X\sqcup Y|=|X|+|Y|.$$
This relation just says that, in order to count a set composed of two smaller sets, we just count each of the smaller sets and add them.
The product $X\times Y$ is the set of pairs $(x,y)$ with $x\in X$ and $y\in Y$. We have the relation
$$|X\times Y|=|X|\cdot |Y|.$$ 
This relation states that, if we wish to count the number of possible combinations of two things, we may count the number of possibilities for each item separately and multiply them. 
This connection is fairly nice because the relations more or less express the way that addition and multiplication are related to counting - and I'd imagine that most everyone has encountered these relations implicitly while learning how (and why) to add and multiply.
