LCS-Baer Lie category

As the category of LCS-Baer Lie rings
The LCS-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 LCS-Baer Lie groups
The LCS-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.