>>567
Not >565 but category theory comes in handy to formulate many concepts, it's a useful language to have. 

For example often one will have already established what a "morphism" is and would like to also have the notion of "isomorphism". Category theory tells one that the latter notion follows from the former while having all the desirable properties. Similiar applies to say the notion of product or coproduct.

This also allows one to develop machinery and tools in the abstarct context of category theory, e.g. homological algebra in Abelian categories, and then apply those tools in many different contexts, e.g. homological algebra for R-modules, or sheaves of R-modules, etc..