I am new, very new, to category theory - which I am trying to learn on my own. I've run across an example in several texts which confuses me.
Specifically, it is the category Mat where objects are natural numbers and morphs between the objects m and n are mxn matrices. I can see that this is a category, but I wonder what it provides an example of. While definitions are neither correct nor incorrect, they can certainly be useful or useless, and this example seems to be in the latter category.
If authors want an example of a category with matrices as morphs, why not let the objects also be matrices, subject only to the restriction that the dimensions are such that post multiplication of a matrix in the domain by a morph gives a matrix in the codomain? This gives a much richer example.
Again, I am not questioning the "correctness" of anything. But when I encounter what seems like a trivial example, used repeatedly, I have to wonder whether I am missing the whole point the author is trying to make.
Thanks for any help or comments.