trivial functor from the category of groups

Notation

!_\Grp: \Grp \to \1

Domain category of groupsCodomain trivial category Related

!_\Set

!_{BG}

!_{\Idem}

Every category $\C$ has a unique functor $!_{\C} : \C \to 1$ into the trivial category. Here, we specify that $\C$ is the category of groups. It is a basic example of a full functor which is not faithful.

Satisfied Properties

Assigned properties

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Deduced properties

is a coreflector
is continuous
is essentially surjective
is right-invertible
is full
preserves monomorphisms
is a reflector
is cocontinuous
preserves epimorphisms
is a left adjoint
preserves terminal objects
is cofinitary
is left exact
preserves products
preserves regular monomorphisms
is dominant
is a right adjoint
preserves initial objects
is finitary
preserves coproducts
is right exact
preserves regular epimorphisms
preserves finite products
is exact
preserves equalizers
is regular
preserves finite coproducts
preserves coequalizers
is coregular
preserves binary products
preserves coreflexive equalizers
preserves binary coproducts
preserves reflexive coequalizers

Unsatisfied Properties

Assigned properties

is not essentially injective

Deduced properties*

is not left-invertible
is not full on isomorphisms
is not an equivalence
is not conservative
is not pseudomonic
is not fully faithful
is not an isomorphism
is not faithful
is not monadic
is not comonadic
is not representable

*This also uses the deduced satisfied properties.

Unknown properties

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