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### 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

 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

 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

 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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