# Definitions for categorificationcat·e·gori·fi·ca·tion

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1. categorificationnoun

A procedure that defines theorems in terms of category theory

### WikipediaRate this definition:0.0 / 0 votes

1. 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. The reverse of categorification is the process of decategorification. Decategorification is a systematic process by which isomorphic objects in a category are identified as equal. Whereas decategorification is a straightforward process, categorification is usually much less straightforward. In the representation theory of Lie algebras, modules over specific algebras are the principal objects of study, and there are several frameworks for what a categorification of such a module should be, e.g., so called (weak) abelian categorifications.Categorification and decategorification are not precise mathematical procedures, but rather a class of possible analogues. They are used in a similar way to the words like 'generalization', and not like 'sheafification'.

### WikidataRate this definition:0.0 / 0 votes

1. 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 isomorphisms of functors satisfying additional properties. The term was coined by Louis Crane. Categorification is the reverse process of decategorification. Decategorification is a systematic process by which isomorphic objects in a category are identified as equal. Whereas decategorification is a straightforward process, categorification is usually much less straightforward, and requires insight into individual situations.

### Numerology

1. Chaldean Numerology

The numerical value of categorification in Chaldean Numerology is: 2

2. Pythagorean Numerology

The numerical value of categorification in Pythagorean Numerology is: 2

## Translations for categorification

• 分类

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"categorification." Definitions.net. STANDS4 LLC, 2024. Web. 13 Jun 2024. <https://www.definitions.net/definition/categorification>.

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