shh.homolalg
Interface KernelledCatMorphism

All Superinterfaces:

Morphism

All Known Subinterfaces:

ExactCategoryMorphism

All Known Implementing Classes:

QvspMorphism

public interface KernelledCatMorphism

extends Morphism

A kernelled category is a weakened version of an exact category. There are zero objects and zero morphisms, and every morphism has a kernel. However, cokernels may not exist. Even if they do, the canonical map from coimage to image may not be an isomorphism. See ExactCategoryMorphism for information to compare with.

Our main example of a kernelled category is the category of free modules of finite rank over a principal ideal domain. The main example we implement is the category of maps Zⁿ &to; Z^m.

Author:

Mark McConnell

See Also:

ExactCategoryMorphism

Method Summary

ExactCategoryMorphism	getCoimage() See the comment on the class.
ExactCategoryMorphism	getCoimSection() See the comment on the class.
ExactCategoryMorphism	getKernel() See the comment on the class.
ExactCategoryMorphism	getKerRetraction() See the comment on the class.
boolean	isCompositionZero(ExactCategoryMorphism f) Like Morphism.compose(shh.homolalg.Morphism), but only tests whether the composition is a zero morphism.
boolean	isZero() Whether this is a zero morphism.

Methods inherited from interface Morphism

compose, getInverse, getSource, getTarget, isEpic, isIsomorphism, isMonic

Method Detail

isZero

public boolean isZero()

Whether this is a zero morphism.

isCompositionZero

public boolean isCompositionZero(ExactCategoryMorphism f)

Like Morphism.compose(shh.homolalg.Morphism), but only tests whether the composition is a zero morphism. Is expected to be more efficient than this.compose(f).isZero(), because it doesn't have to store the composition.

getKernel

public ExactCategoryMorphism getKernel()

See the comment on the class.

getKerRetraction

public ExactCategoryMorphism getKerRetraction()

See the comment on the class.

getCoimage

public ExactCategoryMorphism getCoimage()

See the comment on the class.

getCoimSection

public ExactCategoryMorphism getCoimSection()

See the comment on the class.