embedding of integer into rational numbers
- Notation:
- Category: category of commutative rings
- nLab Link
The inclusion is a typical example of a localization. It is a standard example of a mono- and epimorphism which is not an isomorphism in the category of (commutative) rings.
Satisfied Properties
Assigned properties
- is a monomorphism
- is an epimorphism
Deduced properties
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Unsatisfied Properties
Assigned properties
- is not an isomorphism
Deduced properties*
- is not a split monomorphism
- is not an extremal monomorphism
- is not a split epimorphism
- is not an extremal epimorphism
- is not a strong monomorphism
- is not a strong epimorphism
- is not a strict monomorphism
- is not a strict epimorphism
- is not a regular monomorphism
- is not a regular epimorphism
- is not an effective monomorphism
- is not a normal monomorphism
- is not an effective epimorphism
- is not a normal epimorphism
*This also uses the deduced satisfied properties.
Unknown properties
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Indistinguishable morphisms
These morphisms in the database currently have exactly the same properties as the embedding of integer into rational numbers. This indicates that the data may be incomplete or that a distinguishing property may be missing from the database.