(-2)-category

There is just one *$(-2)$-category*, namely the truth value True. Compare the concepts of (−1)-category (a truth value in general) and 0-category (a set). The point of $(-2)$-categories is that they complete some patterns in the periodic table of $n$-categories. (They also shed light on the theory of homotopy groups and n-stuff.)

For example, there should be a $(-1)$-category of $(-2)$-categories; this is the true truth value. The category of $(-2)$-categories is a monoidal category in a unique way; then a category enriched over this is a $(-1)$-category; such is necessarily an enriched groupoid. If you think of a $(-1)$-category as a 0-poset, then this makes a $(-2)$-category a (−1)-poset. If you think of a $(-1)$-category as a (−1)-groupoid, then this makes a $(-2)$-category a (−2)-groupoid.

For an introduction to $(-1)$-categories and $(-2)$-categories see page 11 of

- John C. Baez, Michael Shulman,
*Lectures on n-Categories and Cohomology*(arXiv).

$(-1)$-categories and $(-2)$-categories were discovered (or invented) by James Dolan and Toby Bartels. To witness these concepts in the process of being discovered, read the discussion here:

- John Baez, Toby Bartels, David Corfield and James Dolan, Property, structure and stuff. See also stuff, structure, property for more on that material.

Last revised on June 30, 2010 at 22:07:26. See the history of this page for a list of all contributions to it.