# Contents

## Idea

A 0-groupoid or 0-type a set. This terminology may seem strange at first, but it is very helpful to see sets as the beginning of a sequence of concepts: sets, groupoids, 2-groupoids, 3-groupoids, etc. Doing so reveals patterns such as the periodic table. (It also sheds light on the theory of homotopy groups and n-stuff.)

For example, there should be a $1$-groupoid of $0$-groupoids; this is the underlying groupoid of the category of sets. Then a groupoid enriched over this is a $1$-groupoid (more precisely, a locally small groupoid). Furthermore, an enriched category is a category (or $1$-category), so a $0$-groupoid is the same as a 0-category.

One can continue to define a (−1)-groupoid to be a truth value and a (−2)-groupoid to be a triviality (that is, there is exactly one).

h-level 2 | 0-truncated | discrete space | 0-groupoid/set | sheaf | h-set h-level 3 | 1-truncated | homotopy 1-type | 1-groupoid/groupoid | (2,1)-sheaf/stack | h-groupoid h-level 4 | 2-truncated | homotopy 2-type | 2-groupoid | | h-2-groupoid h-level 5 | 3-truncated | homotopy 3-type | 3-groupoid | | h-3-groupoid h-level $n+2$ | $n$-truncated | homotopy n-type | n-groupoid | | h-$n$-groupoid | h-level $\infty$ | untruncated | homotopy type | ∞-groupoid | (∞,1)-sheaf/∞-stack | h-$\infty$-groupoid

Revised on September 10, 2012 20:24:12 by Urs Schreiber (131.174.188.17)