A strict -category is a directed 3-graph equipped with a composition operation on adjacent cells (of all levels) which is strictly unital and associative.
A strict -category, often called simply a 3-category, is a category enriched over , the cartesian monoidal category of strict -categories. Similarly, a strict 3-groupoid? is a groupoid enriched over strict 2-groupoids.
These are also called globular strict -categories and -groupoids, to emphasise the underlying geometry.
A strict -category is the same as a strict omega-category which is trivial in degree .