group of units functor

 algebra
Notation (−)×:Mon→Grp(-)^{\times}: \Mon \to \Grp Domain category of monoidsCodomain category of groupsLeft adjoint forgetful functor from groups to monoids External nLab Link

This functor maps a monoid MM to its group of units M×M^{\times}, consisting of pairs (a,b)∈M2(a,b) \in M^2 satisfying ab=ba=1ab=ba=1. Equivalently, it takes the submonoid of invertible elements of MM, equipped with the inverse operation.

Satisfied Properties

Assigned properties

Deduced properties

Unsatisfied Properties

Assigned properties

Deduced properties*

*This also uses the deduced satisfied properties.

Unknown properties

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