Categorification
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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.
Examples of categorification include homology theories in topology.
[edit] Further reading
- John Baez and James Dolan, Categorification, arXiv:math.QA/9802029
- Louis Crane and David N. Yetter, Examples of categorification, Cahiers de Topologie et Géometrie Différentielle Categoriques 39 (1998), no. 1, 3--25.
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