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 $Gr_k$.

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

Last revised on May 27, 2012 at 13:24:17.
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