User talk:78.144.200.148

Carries the structure of a category?
In category theory, a strict 2-category is a category with "morphisms between morphisms", that is, where each hom-set itself carries the structure of a category.

The first bit makes perfect sense but the second bit confuses me. Why would adding morphisms between morphisms allow the hom-set to 'carry the structure of a category'? Doesn't a hom-set already carry the structure? Are objects not part of the structure too? What does 'carry the structure' mean? - perhaps I'm not familiar enough with the terminology.