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Categorification

In mathematics, categorification is the process of replacing set-theoretic theorems with category-theoretic analogues. Categorification, when done successfully, replaces sets with categories, functions with functors, and equations with natural isomorphisms of functors satisfying additional properties. The term was coined by Louis Crane.

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Examples

Abelian categorifications

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Categorification

Nodes52
Edges51
Triples14
Avg. degree1.96
Density0.038462
Components1

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Categorification

Top relations

related to Examples · 11
Categorification → Betti, Emmy Noether, For, In, Khovanov, Later, Less, One, Other, See, This
is a · 2
Categorification → process of decategorification, process of replacing set-theoretic theorems with category-theoretic analogues
related to Further reading · 1
Categorification → Baez

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Important terminology

decategorification process category abelian sets displaystyle theory objects ring analogues module functions numbers group natural categorifications set-theoretic theorems functors isomorphic

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Categorificationis aprocess of replacing set-theoretic theorems with category-theoretic analogues0.90text
Categorificationis aprocess of decategorification0.90text
Categorificationrelated to ExamplesOne0.60section
Categorificationrelated to ExamplesFor0.60section
Categorificationrelated to ExamplesIn0.60section
Categorificationrelated to ExamplesLess0.60section
Categorificationrelated to ExamplesLater0.60section
Categorificationrelated to ExamplesThis0.60section
Categorificationrelated to ExamplesOther0.60section
Categorificationrelated to ExamplesEmmy Noether0.60section
Categorificationrelated to ExamplesBetti0.60section
Categorificationrelated to ExamplesSee0.60section

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