What does categorification mean?

Definitions for categorification
cat·e·gori·fi·ca·tion

This dictionary definitions page includes all the possible meanings, example usage and translations of the word categorification.

Wiktionary

  1. categorificationnoun

    A procedure that defines theorems in terms of category theory

Wikipedia

  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'.

Wikidata

  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.

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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


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

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