The theory of categories and functors abstracts the concepts "object" and "map" from the underlying mathematical fields, for example, from algebra or topology, to investigate which statements can be proved in such an abstract structure. Then these statements will be true in all those mathematical fields which may be expressed by means of this language.
Read more at https://ebookee.org/Categories-and-Functors-Pure-and-Applied-Mathematics-Vol-39-by-Bodo-Pareigis_1912598.html#TU81kkQWC0WWorr7.99