*Category theory* is a branch of abstract mathematics concerned with exposing and describing the underlying structure of logical and mathematical systems. Concepts from category theory have proven to be extremely effective as tools for structuring both the semantics of programming languages and programs themselves. Various category theoretic structures are used as tools for abstraction in programming, including functors, monads, and algebras.

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A category is an embarrassingly simple concept. A category consists of objects and arrows that go between them.


You can get real appreciation for categories by studying a variety of examples. Categories come in all shapes and sizes and often pop up in unexpected places.