Lazard Lie category
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Contents
Definition
As the category of Lazard Lie rings
The Lazard Lie category can be defined as the following concrete category:
Item | Value |
---|---|
Objects | Lazard Lie rings, i.e., Lie rings for which there exists a finite ![]() ![]() ![]() |
Morphisms | Lie ring homomorphisms between Lazard Lie rings. |
Forgetful functor to set | Sends a Lazard Lie ring to its underlying set, sends a homomorphism of Lazard 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 Lazard Lie groups
The Lazard Lie category can be defined as the following concrete category:
Item | Value |
---|---|
Objects | Lazard Lie groups |
Morphisms | homomorphism of groups between Lazard Lie groups. |
Forgetful functor to set | Sends a Lazard Lie group to its underlying set, sends a homomorphism of Lazard 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 Lazard Lie category