n-category number

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In mathematics, the category number of a mathematician is a humorous construct invented by Dan Freed, {{cite journal|last1=Freed|first1=Dan|title=The Verlinde Algebra is Twisted Equivariant K-Theory|journal=Turkish Journal of Mathematics|date=2001|volume=25|issue=1|pages=159–167|arxiv=math/0101038 |bibcode=2001math......1038F }} {{cite web|last1=Freed|first1=Dan|url=https://www.ma.utexas.edu/users/dafr/MSRI_25.pdf|title=Remarks on Chern-Simons Theory|accessdate=8 August 2016}}

intended to measure the capacity of that mathematician to stomach the use of higher categories. It is defined as the largest number n such that they can think about n-categories for a half hour without getting a splitting headache.