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category theory
Sign in to savebranch of mathematics studying categories, functors, and natural transformations
Category theory is a branch of mathematics that studies abstract structures called categories, along with the relationships between them (functors) and relationships between those relationships (natural transformations). It matters because it provides a powerful language for connecting different areas of mathematics and science by focusing on how things relate to each other rather than their internal details.
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Schematic representation of three objects and three morphisms of a category, which form a commutative diagram
Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the mid-20th century in their foundational work on algebraic topology. Category theory can be used in most areas of mathematics. In particular, many constructions of new mathematical objects from previous ones that appear similarly in several contexts are conveniently expressed and unified in terms of categories. Examples include quotient spaces, direct products, completion, and duality.