LCS-Lazard Lie category

As the category of Lazard Lie rings
The Lazard 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-Lazard Lie groups
The LCS-Lazard Lie category can be defined as the following concrete category:

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