Category theory is a branch of mathematics that explores and formalizes abstract structures and relationships between them. It provides a unified framework for understanding different areas of mathematics by focusing on the objects and morphisms (arrows) between them, rather than the internal details of each individual structure.

And introduce the concept of FUNCTOR

Another great example is vector space and dual vector space

note it’s contravariant functors, similarly, later on cohomology follows the same.

then there is a concept of transforming functors

special form is natural transformation.