trivial functor from the category of groups
- notation:
- Source: category of groups
- Target: trivial category
- Related functors:
Every category has a unique functor into the trivial category. Here, we specify that is the category of groups. It is a basic example of a full functor which is not faithful.
Satisfied Properties
Assigned properties
- is a coreflector
- is a reflector
- is full
Deduced properties
- is a left adjoint
- is right-invertible
- is a right adjoint
- is continuous
- is essentially surjective
- is cocontinuous
- is cofinitary
- is left exact
- preserves products
- is dominant
- 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
- 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 monadic
- is not comonadic
- is not faithful
- is not representable
*This also uses the deduced satisfied properties.
Unknown properties
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