Meaning of group functor | Babel Free

Definitions

A group object that is an object in a category of functors; a functor with certain properties that generalise the concept of group.

Examples

“In order to be able to efficiently state the main results of this chapter (in §4) we formulate here a group-functor version of the R-nilpotent tower lemma (Ch.III, 6.4).”

“A direct product of k–group functors is again a k–group functor; so is a fibre product if the morphisms used in its construction are homomorphisms of k–group functors.”

“By a group functor we mean a functor from small k-algebras to groups. A homomorphism of group functors is a natural transformation. A subgroup functor of a group functor G is a subfunctor H such that H(R) is a subgroup of G(R) for all R; it is normal if H(R) is normal in G(R) for all R.”

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