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mixed up extremal and regular
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Dominic van der Zypen
Dominic van der Zypen
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Regular Extremal, but not extremalregular monomorphism

Is there an example of a category, and a monomorphism $m:X\to Y$ between two objects such that $m$ is regularextremal, but not extremalregular? (A monomorphism $m:X\to Y$ is said to be extremal if whenever $m=g\circ e$ with $e$ an epimorphism, then $e$ is an isomorphism.)

Regular, but not extremal monomorphism

Is there an example of a category, and a monomorphism $m:X\to Y$ between two objects such that $m$ is regular, but not extremal? (A monomorphism $m:X\to Y$ is said to be extremal if whenever $m=g\circ e$ with $e$ an epimorphism, then $e$ is an isomorphism.)

Extremal, but not regular monomorphism

Is there an example of a category, and a monomorphism $m:X\to Y$ between two objects such that $m$ is extremal, but not regular? (A monomorphism $m:X\to Y$ is said to be extremal if whenever $m=g\circ e$ with $e$ an epimorphism, then $e$ is an isomorphism.)

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Dominic van der Zypen
Dominic van der Zypen
  • 48.8k
  • 8
  • 47
  • 161

Regular, but not extremal monomorphism

Is there an example of a category, and a monomorphism $m:X\to Y$ between two objects such that $m$ is regular, but not extremal? (A monomorphism $m:X\to Y$ is said to be extremal if whenever $m=g\circ e$ with $e$ an epimorphism, then $e$ is an isomorphism.)