category theory

category theory
A branch of mathematics which deals with spaces and maps between them in abstraction, taking similar theorems from various disparate more concrete branches of mathematics and unifying them.

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  • Category theory — In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them: it abstracts from sets and functions to objects and morphisms . Categories now appear in most branches of mathematics and in… …   Wikipedia

  • Outline of category theory — The following outline is provided as an overview of and guide to category theory: Category theory – area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as… …   Wikipedia

  • List of category theory topics — This is a list of category theory topics, by Wikipedia page. Specific categories *Category of sets **Concrete category *Category of vector spaces **Category of graded vector spaces *Category of finite dimensional Hilbert spaces *Category of sets… …   Wikipedia

  • Monad (category theory) — For the uses of monads in computer software, see monads in functional programming. In category theory, a branch of mathematics, a monad, Kleisli triple, or triple is an (endo )functor, together with two natural transformations. Monads are used in …   Wikipedia

  • Higher category theory — is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities. Contents 1 Strict higher categories 2 Weak higher… …   Wikipedia

  • Timeline of category theory and related mathematics — This is a timeline of category theory and related mathematics. By related mathematics is meant first hand * Homological algebra * Homotopical algebra * Topology using categories, especially algebraic topology * Categorical logic * Foundations of… …   Wikipedia

  • Cone (category theory) — In category theory, a branch of mathematics, the cone of a functor is an abstract notion used to define the limit of that functor. Cones make other appearances in category theory as well. Contents 1 Definition 2 Equivalent formulations 3 Category …   Wikipedia

  • Nerve (category theory) — In category theory, the nerve N(C) of a small category C is a simplicial set constructed from the objects and morphisms of C. The geometric realization of this simplicial set is a topological space, called the classifying space of the category C …   Wikipedia

  • Kernel (category theory) — In category theory and its applications to other branches of mathematics, kernels are a generalization of the kernels of group homomorphisms and the kernels of module homomorphisms and certain other kernels from algebra. Intuitively, the kernel… …   Wikipedia

  • Diagram (category theory) — In category theory, a branch of mathematics, a diagram is the categorical analogue of an indexed family in set theory. The primary difference is that in the categorical setting one has morphisms. An indexed family of sets is a collection of sets …   Wikipedia

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