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Monad (functional programming) — In functional programming, a monad is a programming structure that represents computations. Monads are a kind of abstract data type constructor that encapsulate program logic instead of data in the domain model. A defined monad allows the… … 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
Beck's monadicity theorem — In category theory, a branch of mathematics, Beck s monadicity theorem asserts that a functor :U: C o Dis monadic if and only if # U has a left adjoint; # U reflects isomorphisms; and # C has coequalizers of U split coequalizer pairs, and U… … Wikipedia
Adjoint functors — Adjunction redirects here. For the construction in field theory, see Adjunction (field theory). For the construction in topology, see Adjunction space. In mathematics, adjoint functors are pairs of functors which stand in a particular… … Wikipedia
Background and genesis of topos theory — This page gives some very general background to the mathematical idea of topos. This is an aspect of category theory, and has a reputation for being abstruse. The level of abstraction involved cannot be reduced beyond a certain point; but on the… … 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
Roger Godement — (born in 1921) is a French mathematician, known for his work in functional analysis, and also his expository books.He started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan. He started research… … Wikipedia
Coherent duality — In mathematics, coherent duality is any of a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex manifold theory, as well as some aspects of commutative algebra that are part of the local… … 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
