Baer Lie category

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

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:

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