nLab codimension

Idea

A subobject of dimension $k$ inside an object of dimension $d$ is said to have codimension $d-k$.

Examples

• A submanifold of dimension 3 inside a manifold of dimension 5 has codimension 5-3.

• In algebraic geometry a subvariety? of codimension 1 is called a divisor (algebraic geometry).