An arrow here is not a matrix, but it's represented as a matrix, in this picture. Just a convenient way to show how it works if domain is a union and codomain is a product.
I'd suggest to go in the opposite direction, and consider a category where objects are natural numbers, and arrows are matrices n×m (a matrix from [n] to [m]). You can check that it's a category. Similarly, "multiply by a given number" can be considered as an arrow from [1] to [1] in this category.
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I'd suggest to go in the opposite direction, and consider a category where objects are natural numbers, and arrows are matrices n×m (a matrix from [n] to [m]). You can check that it's a category. Similarly, "multiply by a given number" can be considered as an arrow from [1] to [1] in this category.
no subject