opposite monoid functor
- notation:
- Source: category of monoids
- Target: category of monoids
- Left adjoint functor:
- Right adjoint functor:
- Related functors:
- nLab Link
This functor maps a monoid to its opposite monoid which has the multiplication . A monoid homomorphism is also a monoid homomorphism .
Satisfied Properties
Assigned properties
- is an isomorphism
Deduced properties
- is an equivalence
- is essentially surjective
- is fully faithful
- is left-invertible
- is right-invertible
- is monadic
- is a reflector
- is comonadic
- is a coreflector
- is a left adjoint
- is faithful
- is full
- is conservative
- is essentially injective
- is dominant
- is a right adjoint
- is continuous
- is full on isomorphisms
- is cocontinuous
- is cofinitary
- is left exact
- preserves products
- is pseudomonic
- is finitary
- preserves coproducts
- is right exact
- preserves finite products
- is exact
- preserves equalizers
- preserves monomorphisms
- preserves finite coproducts
- preserves coequalizers
- preserves epimorphisms
- preserves binary products
- preserves terminal objects
- preserves coreflexive equalizers
- preserves regular monomorphisms
- preserves binary coproducts
- preserves initial objects
- preserves reflexive coequalizers
- preserves regular epimorphisms
- is regular
- is coregular
Unsatisfied Properties
Assigned properties
—
Deduced properties*
- is not representable
*This also uses the deduced satisfied properties.
Unknown properties
—
Undistinguishable functors
These functors in the database currently have exactly the same properties as the opposite monoid functor. This indicates that the data may be incomplete or that a distinguishing property may be missing from the database.