In mathematics, categorification refers to the process of replacing set theory theorems by category theory analogues. Categorification, when done successfully, replaces set (mathematics)s by category (category theory), function (mathematics)s with functors, and equations by natural transformation 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 morphism objects in a category are identified as equality. Whereas decategorification is a straightforward process, categorification is usually much less straightforward, and requires insight into individual situations.

Examples of categorification include homology theory in topology.

=Further reading=