nLab
Demazure, lectures on p-divisible groups, II.1, group -functors

This entry is about a section of the text

• Michel Demazure, lectures on p-divisible groups, web

A group functor is a group object in a functor category.

A $k$-group functor is a k-functor? which is a group functor.

A group functor which is a scheme is called $k$-group scheme or just $k$-group. The category of $k$-groups is denoted by ${\mathrm{Gr}}_k$.

Terminology

The terminology of group-functors is mainly used in the theory of algebraic groups in algebraic geometry. If $G$ is a group functor the multiplication morphism $\pi :G\times G\to G$ is called group law on $G$.

References

• Michel Demazure, lectures on p-divisible groups web, chapter II