Yes, roughly. You can think about a category like a group which carries around "type parameters" to say which "elements" you can and can't multiply. Also, "elem

Yes, roughly. You can think about a category like a group which carries around "type parameters" to say which "elements" you can and can't multiply. Also, "elements" may not be invertible. For example, for each N, there is a group of invertible N by N matrices. If we want to allow non-square matrices too, we can bundle them up as a category: - The objects are the natural numbers - A map from N to M is an M row by N column matrix - We compose A : N -> M and B : M -> K by multiplying them as matrices to get BA : N -> K. The objects (i.e., the dimensions) are type checking which things we can and can't multiply