Baer Lie category

Definition

As the category of Baer Lie rings

The Baer Lie category can be defined as the following concrete category:

Item	Value
Objects	Baer Lie rings, i.e., Lie rings that are uniquely 2-divisible and have class at most two
Morphisms	Lie ring homomorphisms between Baer Lie rings. Note that a Lie ring homomorphism automatically preserves the unique 2-division.
Forgetful functor to set	Sends a Baer Lie ring to its underlying set, sends a homomorphism of Baer Lie rings to the map of underlying sets.

Viewed this way, the category is a full subcategory of the category of Lie rings.

As the category of Baer Lie groups

The Baer Lie category can be defined as the following concrete category:

Item	Value
Objects	Baer Lie groups, i.e., groups that are uniquely 2-divisible and have class at most two
Morphisms	homomorphism of groups between Baer Lie groups. This automatically preserves the unique 2-division.
Forgetful functor to set	Sends a Baer Lie group to its underlying set, sends a homomorphism of Baer Lie groups to the map of underlying sets.

Viewed this way, the category is a full subcategory of the category of groups.

Equivalence of definitions

Further information: equivalence of definitions of Baer Lie category