walking morphism representation
This is the functor that maps the universal morphism to the unique map in . It provides a very simple example of a functor that preserves coequalizers (and hence regular epimorphisms) but does not preserve epimorphisms.
Satisfied properties
Assigned properties
- is representable
- is fully faithful
- preserves initial objects
- is finitary
Deduced properties
- is a right adjoint
- is continuous
- preserves equalizers
- preserves coreflexive equalizers
- is faithful
- is full
- is conservative
- preserves coequalizers
- preserves reflexive coequalizers
- is cofinitary
- is left exact
- preserves products
- preserves regular monomorphisms
- is full on isomorphisms
- is monadic
- is left-invertible
- preserves regular epimorphisms
- preserves finite products
- preserves monomorphisms
- is regular
- is essentially injective
- is pseudomonic
- preserves binary products
- preserves terminal objects
Unsatisfied properties
Assigned properties
- does not preserve epimorphisms
- is not dominant
Deduced properties*
- is not essentially surjective
- is not right exact
- is not an equivalence
- is not exact
- is not right-invertible
- is not cocontinuous
- does not preserve finite coproducts
- is not coregular
- is not a reflector
- is not an isomorphism
- is not a left adjoint
- is not a coreflector
- does not preserve coproducts
- does not preserve binary coproducts
- is not comonadic
*This also uses the deduced satisfied properties.
Unknown properties
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