split epimorphism
A morphism is a split epimorphism if there is a morphism with . Split epimorphisms are also called retractions.
Relevant implications
Examples
There are 4 morphisms with this property.
- identity map of a group
- identity map of a set
- map into the singleton set
- universal split epimorphism
Counterexamples
There are 11 morphisms without this property.
- Baer-Specker relations
- embedding of A3 into S3
- embedding of integers into rational numbers
- example of a non-strong extremal monomorphism
- handle of the universal fork
- inclusion of positive numbers
- map from the empty set
- multiplication by 2
- presentation of the walking idempotent
- reduction modulo p
- universal morphism
Unknown
There are 0 morphisms for which the database has no information on whether they satisfy this property.
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