Category theory | Algebraic topology

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'. (Wikipedia).

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From playlist Mathematics

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From playlist Mathematics

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From playlist Metacognition

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From playlist R Tutorial | Rstudio

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From playlist Mathematics

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From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory

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From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"

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From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory

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From playlist Mathematics

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From playlist Toposes online

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From playlist Workshop: Monoidal and 2-categories in representation theory and categorification

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