# Supergroup (physics)

More formally, a Lie supergroup is a supermanifold G together with a multiplication morphism $\mu :G \times G\rightarrow G$, an inversion morphism $i : G \rightarrow G$ and a unit morphism $e: 1 \rightarrow G$ which makes G a group object in the category of supermanifolds. This means that, formulated as commutative diagrams, the usual associativity and inversion axioms of a group continue to hold. Since every manifold is a super manifold, a Lie supergroup generalises the notion of a Lie group.