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

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

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

A group functor which is a scheme is called kk-group scheme or just kk-group. The category of kk-groups is denoted by Gr kGr_k.


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


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

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