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    Category theory

    Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Category theory is used in almost all 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. Many areas of computer science also rely on category theory, such as functional programming and semantics. A category is formed by two sorts of objects: the objects of the category, and the morphisms, which relate two objects called the source and the target of the morphism. Metaphorically, a morphism is an arrow that maps its source to its target. Morphisms can be composed if the target of the first morphism equals the source of the second one. Wikipedia

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  2. en.wikipedia.org

    Category theory is a general theory of mathematical structures and their relations, introduced by Eilenberg and Mac Lane in algebraic topology. Learn the basic concepts of categories, morphisms, functors, and natural transformations, and their applications in various fields of mathematics and computer science.
  3. plato.stanford.edu

    Category theory has come to occupy a central position in contemporary mathematics and theoretical computer science, and is also applied to mathematical physics. Roughly, it is a general mathematical theory of structures and of systems of structures. As category theory is still evolving, its functions are correspondingly developing, expanding ...
  4. Category theory is a relatively new branch of mathematics that has transformed much of pure math research. The technical advance is that category theory provides a framework in which to organize formal systems and by which to translate between them, allowing one to transfer knowledge from one field to another. But this same organizational framework also has many compelling examples outside of ...
  5. Learn the definition and properties of categories, functors, and natural transformations, and see how they apply to representation theory and other areas of mathematics. This web page is a part of a course on introduction to representation theory at MIT.
  6. web.math.ucsb.edu

    A set of notes for a graduate student learning seminar on category theory, covering basic definitions, examples, diagrams, functors, natural transformations, limits, colimits, adjoints and monads. The notes are written by Daniel Epelbaum and Ashwin Trisal and available as a PDF file.
  7. en.wikibooks.org

    Category theory was invented by Samuel Eilenberg and Saunders Mac Lane in the 1940s as a way of expressing certain constructions in algebraic topology. Category theory was developed rapidly in the subsequent decades. It has become an autonomous part of mathematics, studied for its own sake as well as being widely used as a unified language for ...
  8. pi.math.cornell.edu

    A comprehensive introduction to category theory, covering topics such as the Yoneda lemma, adjunctions, limits, colimits, monads, and abelian categories. The notes are based on lectures by Peter Johnstone, a leading expert in the field, and include exercises and references.

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