identity map of a set
Every object of a category has an identity morphism. In this case, we take a set and consider its identity morphism in . To decide all of its properties, we assume that has at least two elements.
Satisfied properties
Assigned properties
- is an isomorphism
Deduced properties
- is an effective monomorphism
- is a split monomorphism
- is an effective epimorphism
- is a split epimorphism
- is a regular monomorphism
- is a regular epimorphism
- is a strict monomorphism
- is a strict epimorphism
- is a strong monomorphism
- is a strong epimorphism
- is an extremal monomorphism
- is an extremal epimorphism
- is a monomorphism
- is an epimorphism
Unsatisfied properties
Assigned properties
- is not constant
- is not coconstant
Deduced properties*
- is not a zero morphism
- is not a normal monomorphism
- is not a normal epimorphism
*This also uses the deduced satisfied properties.
Unknown properties
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