Category theory MOC

Categorification

Categorification¹ s a broad approach of adding (higher) category structure to an algebra, usually so that what once were elements become objects. Usually a categorification is some canonical but non-unique section to decategorization, where we forget -morphisms and replace -isomorphisms with equalities.

• One particularly prevalent approach of categorification is Internalization to the category of categories.

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Footnotes

1. sometimes called, vertical categorification, in contrast to oidification or horizontal categorification. ↩