GAP (homalg) - Appendix F: Overview of the homalg Package Source Code

The homalg package reached more than 50.000 lines of GAP4 code (excluding the documentation) before the first release was made. To keep this amount of code tracebale, the package was split in several files.

F.1 The Basic Objects

**Table:** *The **homalg** package files (continued)*
Filename `.gd`/`.gi`	Content
`HomalgObject`	objects of Abelian categories

`HomalgSubobject`	subobject of objects of Abelian categories

`HomalgMorphism`	morphisms of Abelian categories

`HomalgElement`	elements are morphisms from "structure objects"

`HomalgFiltration`	filtrations of objects of Abelian categories

`HomalgComplex`	(co)complexes of objects or of (co)complexes

`HomalgChainMorphism`	chain morphisms of (co)complexes
	consisting of morphisms or chain morphisms

`HomalgBicomplex`	bicomplexes of objects or of (co)complexes

`HomalgBigradedObject`	(differential) bigraded objects

`HomalgSpectralSequence`	homological and cohomological
	spectral sequences

`HomalgFunctor`	constructors of (multi) functors of
	Abelian categories,
	left derivation of covariant functors,
	right derivation of contravariant functors,
	left satellites of covariant functors,
	right satellites of contravariant functors,
	and composition of functors

`HomalgDiagram`	basic diagrams

F.2 The High Level Homological Algorithms

**Table:** *The **homalg** package files (continued)*
Filename `.gd`/`.gi`	Content
`StaticObjects`	subfactors, syzygy objects, shorten resolutions,
	saturations

`Morphisms`	resolutions, (co)kernel sequences

`Complexes`	(co)homology, horse shoe lemma, connecting
	homomorphisms, Cartan-Eilenberg resolution

`ChainMorphisms`	(co)homology

`SpectralSequences`	Grothendieck bicomplexes associated to two
	composable functors, spectral sequences
	of bicomplexes, Grothendieck spectral sequences
`Filtrations`	spectral filtrations, i.e. filtrations induced
	by spectral sequences of bicomplexes,
	purity filtration

`ToolFunctors`	composition, addition, substraction,
	stacking, augmentation, and post dividing maps
`BasicFunctors`	kernel, defect of exactness
`OtherFunctors`	torsion submodule, torsion free factor,
	pullback, pushout, Auslander dual

F.3 Logical Implications for homalg Objects

**Table:** *The **homalg** package files (continued)*
Filename `.gd`/`.gi`	Content
`LIOBJ`	logical implications for objects of an Abelian category

`LIMOR`	logical implications for morphisms of an Abelian category

`LICPX`	logical implications for complexes

F Overview of the homalg Package Source Code

F.1 The Basic Objects

F.2 The High Level Homological Algorithms

F.3 Logical Implications for homalg Objects