[[Category theory MOC]]
# Categorification

**Categorification**[^aka] s a broad approach of adding [[Higher category|(higher) category]] structure to an algebra,
usually so that what once were elements become objects.
Usually  a categorification is some canonical but non-unique [[Split epimorphism|section]] to [[decategorization]], where we forget $k$-morphisms and replace $k$-isomorphisms with equalities.

  [^aka]: sometimes called, **vertical categorification**, in contrast to [[Oidification|oidification or horizontal categorification]].

- One particularly prevalent approach of categorification is [[Internalization to the category of categories]].

#
---
#state/develop | #lang/en | #SemBr