> 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.
Two mappings with corresponding domain/codomain have to compose by definition of a category. It's not something you can specify.
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.