Category theory is a field of **Mathematics**: topology, geometry, algebra, logic, computer sciences, physics and more are using methods of category theory.

Category theory is a **synthesis** for many structures: sets, preorders, posets, total orders, well-orders, equivalence relations, monoids, groups, groupoids, path algebras of graphs, and more are all examples of categories.

Category theory is a **classification tool**: the collections of sets, posets, monoids, groups, abelian groups, vector spaces, topological spaces, manifolds, chain complexes, and pretty much any kind of mathematical structure do form categories.
Most importantly, the collection of categories themselves is a category.

Category theory is a **language**: morphisms, isomorphisms, endomorphisms, monomorphisms, epimorphisms, functors, diagrams, natural transformations, and many other notions help to organize the relationships between mathematical objects.

Category theory is a **calculus**: limits and colimits, monoidal structures and internal homs, universal properties, adjunctions, presheaves, and many other notions provide general tools to operate on the objects of a category.

And so much more:
category theory is a **geometry** (any category behave like a space);
category theory is a **linear algebra** (categories behave like vector spaces);
category theory is a **logic** (any category has an internal logical language);
category theory is a **philosophy** (categories are the Kantian Transcendental Æsthetics of mathematics);
Category theory is an **art de vivre** (surtout avec un saucisson bien sec)...