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[parent] extremal monomorphism (Definition)
Definition 1   A monomorphism $ m$ in a category $ \mathcal{A}$ is called extremal if the following holds: Whenever $ m=f\circ e$, where $ e$ is an epimorphism, then $ e$ is an isomorphism.

Dual notion: An epimorphism $ e$ is called extremal if the following holds: Whenever $ e=m\circ f$, with $ m$ a monomorphism, then $ m$ is an isomorphism.



"extremal monomorphism" is owned by kompik.
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See Also: properties of regular and extremal monomorphisms, monic

Also defines:  extremal epimorphism

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Cross-references: isomorphism, category, monomorphism
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This is version 3 of extremal monomorphism, born on 2006-06-30, modified 2006-06-30.
Object id is 8116, canonical name is ExtremalMonomorphism.
Accessed 1238 times total.

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AMS MSC: 18A05 (Category theory; homological algebra :: General theory of categories and functors :: Definitions, generalizations)
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