‣ SomeProjectiveObjectForKernelObject( alpha ) | ( attribute ) |
Returns: an object
The argument is a morphism \alpha. The output is the source of EpimorphismFromSomeProjectiveObjectForKernelObject applied to \alpha.
‣ EpimorphismFromSomeProjectiveObjectForKernelObject( alpha ) | ( attribute ) |
Returns: a morphism in \mathrm{Hom}(P,\mathrm{KernelObject}( \alpha ))
The argument is a morphism \alpha. The output is an epimorphism \pi: P \rightarrow \mathrm{KernelObject}( \alpha ) with P a projective object.
‣ EpimorphismFromSomeProjectiveObjectForKernelObjectWithGivenSomeProjectiveObjectForKernelObject( alpha ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}(P,\mathrm{KernelObject}( \alpha ))
The arguments are a morphism \alpha and an object P = \mathrm{SomeProjectiveObjectForKernelObject}( \alpha ). The output is an epimorphism \pi: P \rightarrow \mathrm{KernelObject}( \alpha ).
‣ SomeInjectiveObjectForCokernelObject( alpha ) | ( attribute ) |
Returns: an object
The argument is a morphism \alpha. The output is the range of MonomorphismToSomeInjectiveObjectForCokernelObject applied to \alpha.
‣ MonomorphismToSomeInjectiveObjectForCokernelObject( alpha ) | ( attribute ) |
Returns: a morphism in \mathrm{Hom}(\mathrm{CokernelObject}( \alpha ), I)
The argument is a morphism \alpha. The output is a monomorphism \iota: \mathrm{CokernelObject}( \alpha ) \rightarrow I with I an injective object.
‣ MonomorphismToSomeInjectiveObjectForCokernelObjectWithGivenSomeInjectiveObjectForCokernelObject( alpha ) | ( operation ) |
Returns: a morphism in \mathrm{Hom}(\mathrm{CokernelObject}( \alpha ), I)
The arguments are a morphism \alpha and an object I = \mathrm{SomeInjectiveObjectForCokernelObject}( \alpha ). The output is a monomorphism \iota: \mathrm{CokernelObject}( \alpha ) \rightarrow I.
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