- categorification
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A procedure that defines theorems in terms of category theory
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categorification
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Categorification — In mathematics, categorification refers to the process of replacing set theoretic theorems by category theoretic analogues. Categorification, when done successfully, replaces sets by categories, functions with functors, and equations by natural… … Wikipedia
Mikhail Khovanov — is a professor of mathematics at Columbia University. He earned a PhD[1] in mathematics from Yale University in 1997, where he studied under Igor Frenkel.[2] His interests include knot theory and algebraic topology. He is most well known for the… … Wikipedia
Khovanov homology — In mathematics, Khovanov homology is a homology theory for knots and links. It may be regarded as a categorification of the Jones polynomial. It was developed in the late 1990s by Mikhail Khovanov, then at the University of California, Davis, now … Wikipedia
Function (mathematics) — f(x) redirects here. For the band, see f(x) (band). Graph of example function, In mathematics, a function associates one quantity, the a … Wikipedia
Combinatorial proof — In mathematics, the term combinatorial proof is often used to mean either of two types of proof of an identity in enumerative combinatorics that either states that two sets of combinatorial configurations, depending on one or more parameters,… … Wikipedia
List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… … Wikipedia
Morse homology — In mathematics, specifically in the field of differential topology, Morse homology is a homology theory defined for any smooth manifold. It is constructed using the smooth structure and an auxiliary metric on the manifold, but turns out to be… … Wikipedia
David Corfield — is a philosopher specializing in mathematics and psychology. He is the author of Towards a Philosophy of Real Mathematics (2003), in which he argues that the philosophical implications of mathematics did not stop with Kurt Gödel s incompleteness… … 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
Théorie des catégories — La théorie des catégories étudie les structures mathématiques et les relations qu elles entretiennent. Les catégories sont utilisées dans la plupart des branches mathématiques et dans certains secteurs de l informatique théorique et en… … Wikipédia en Français
