presentation of the walking idempotent
Let denote the walking morphism and denote the walking idempotent. In this entry, we consider the functor that sends the universal morphism to the universal idempotent and view as a morphism in . It provides an example of a strong epimorphism which is not strict.
Satisfied Properties
Assigned properties
- is a strong epimorphism
Deduced properties
- is an extremal epimorphism
- is an epimorphism
Unsatisfied Properties
Assigned properties
- is not a strict epimorphism
- is not constant
- is not coconstant
Deduced properties*
- is not a zero morphism
- is not a regular epimorphism
- is not a split epimorphism
- is not an effective epimorphism
- is not a normal epimorphism
- is not an isomorphism
- is not a split monomorphism
- is not an extremal monomorphism
- is not a monomorphism
- is not a strong monomorphism
- is not a strict monomorphism
- is not a regular monomorphism
- is not an effective monomorphism
- is not a normal monomorphism
*This also uses the deduced satisfied properties.
Unknown properties
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