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Category theory is a way of studying mathematics in terms of structures and relations between them. The mother category theory is the theory of set and functions. Other prototypical examples are linear algebra, topology and all the theories included in the abstract algebra.

In simple terms, a category consists of two parts:

  • the objects of the category
  • the morphisms between the objects of the category

There are also relations between categories: a mathematcal application (functions or maps) from category-one to category-two is called functor if the relation sends objects into objects and morphisms into morphisms.