| 21. | For sets and vector spaces, every epimorphism is a split epimorphism, but this property is wrong for most common algebraic structures.
|
| 22. | For projective resolutions, this condition is almost invisible : a projective pre-cover is simply an epimorphism from a projective module.
|
| 23. | For example, whether or not a morphism of sheaves is a monomorphism, epimorphism, or isomorphism can be tested on the stalks.
|
| 24. | Every epimorphism in this algebraic sense is an epimorphism in the sense of category theory, but the converse is not true in all categories.
|
| 25. | Every epimorphism in this algebraic sense is an epimorphism in the sense of category theory, but the converse is not true in all categories.
|
| 26. | This is an exact sequence because the image 2 "'Z "'of the monomorphism is the kernel of the epimorphism.
|
| 27. | Conversely an epimorphism is called " normal " ( or " conormal " ) if it is the cokernel of some morphism.
|
| 28. | A category is called " conormal " if every epimorphism is normal ( e . g . the category of groups is conormal ).
|
| 29. | The most basic example of an epimorphism ( category theory meaning ), which is not surjective, is the "'Q " '.
|
| 30. | For a morphism f \ colon B \ to A, this is precisely what it means for " f " to be an epimorphism.
|
