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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

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

 


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