morphism endpoints inclusion
This is the functor that embeds the discrete category into the walking morphism . It provides an example of a faithful functor that is full on isomorphisms but not full.
Satisfied properties
Assigned properties
Deduced properties
- is cofinitary
- is left exact
- preserves products
- preserves equalizers
- preserves coreflexive equalizers
- is essentially injective
- is dominant
- is conservative
- preserves monomorphisms
- is finitary
- preserves coproducts
- is right exact
- preserves coequalizers
- preserves reflexive coequalizers
- preserves epimorphisms
- preserves finite products
- is exact
- preserves regular monomorphisms
- is faithful
- preserves finite coproducts
- preserves regular epimorphisms
- preserves binary products
- preserves terminal objects
- is regular
- is pseudomonic
- preserves binary coproducts
- preserves initial objects
- is coregular
Unsatisfied properties
Assigned properties
- is not left-invertible
- is not right-invertible
- is not a right adjoint
- is not a left adjoint
Deduced properties*
- is not a reflector
- is not an equivalence
- is not monadic
- is not a coreflector
- is not comonadic
- is not fully faithful
- is not an isomorphism
- is not full
- is not representable
*This also uses the deduced satisfied properties.
Unknown properties
—