Unit group functor

From Apstheory

[edit] Definition

The unit group of a unital ring is the group of invertible elements with respect to the multiplication operation in the ring. A homomorphism of rings induces a homomorphism of their corresponding unit groups, and this defines a functor from the category of unital rings to the category of groups.

The unit group functor associated with an APS functor to the category of rings is simply a composition of that functor with the functor sending a ring to its unit group.

For instance, the GL IAPS is obtained as the unit group functor corresponding to the matrix IAPS.