Implication details
Claim: If a morphism is a regular monomorphism, then it is a strict monomorphism.
Proof: Let be the equalizer of . In particular, is a monomorphism. Let be a morphism that equalizes all pairs that are equalized by . In particular, equalizes , i.e. . By definition of an equalizer, this means that factors through .
This implication has a dual.
Show 14 morphisms using this implication
- embedding of A3 into S3
- map from the empty set
- example of a non-strong extremal monomorphism
- handle of the universal fork
- identity map of a group
- identity map of a set
- inclusion of positive numbers
- embedding of integers into rational numbers
- multiplication with 2
- reduction modulo p
- map into the singleton set
- universal morphism
- universal split epimorphism
- presentation of the walking idempotent