> you can also specify that two mappings compose
Two mappings with corresponding domain/codomain have to compose by definition of a category. It's not something you can specify.
> you can also specify that two mappings compose
Two mappings with corresponding domain/codomain have to compose by definition of a category. It's not something you can specify.
Yes. When you are specifying a system you are building the category that you want it to live in.
That is probably what they mean by specifying that they compose.
If all you know is that you have two mappings you don't know they compose, until you get the additional information about their sources and targets. In a way that's what the source and targets are: just labels of what you can compose them with.