| 11. | A strong monomorphism satisfies a certain lifting property with respect to commutative squares involving an epimorphism.
|
| 12. | Eventually the monomorphism concept of Louis Pasteur was accepted by the scientific community in the 1950s.
|
| 13. | A "'split monomorphism "'is an homomorphism that has a right inverse.
|
| 14. | In short, the property of being a monomorphism is dual to the property of being an epimorphism.
|
| 15. | In many categories it is possible to write every morphism as the composition of an epimorphism followed by a monomorphism.
|
| 16. | This is also an example of a ring homomorphism which is both a monomorphism and an epimorphism, but not an isomorphism.
|
| 17. | In the context of abstract algebra or universal algebra, a "'monomorphism "'is an injective homomorphism.
|
| 18. | For sets and vector spaces, every monomorphism is a split homomorphism, but this property is wrong for most common algebraic structures.
|
| 19. | For example, whether or not a morphism of sheaves is a monomorphism, epimorphism, or isomorphism can be tested on the stalks.
|
| 20. | :Wouldn't an " isomorphism into " a group just be a monomorphism ( i . e . an injective homomorphism )?
|
