Organic Food is good for you?

It seems that some scientists have just shown that not only do organic foods like Tomatoes have far fewer industrial toxins in them, they also have far more of the good stuff that nutritionists say you should have.

Categorical Problems.

Okay, here's the current thing I'm trying to figure out in the definition of a category. The concept of 'commuting' seems to be undecidable in many cases. For example, lets assume I have a concrete category with three objects, which we'll decide are the integers 1, 2, and 3. Our arrows are functions and the identity function for each object is just f(x)=x. Now, let us assume that we have three particular functions for arrows in mind. f:1->2, g:2->3, and h:1->3.

I am told that the diagram of this category 'commutes' if gf=h. How am I supposed to know that? gf and h are both general functions and the question of whether two general functions are equal is undecidable. Despite this, I find many example given where the arrows are functions and they talk about commuting properties. What gives?