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HigherHomologicalAlgebra 

Higher Homological Algebra

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Introduction

The repository is a collection of the Gap packages. The aim of these packages is to carry out categorical and homological constructions on complexes, homotopy or derived categories. The main focus is the construction of derived equivalences that arise via full strong exceptional collections.

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Packages of HigherHomologicalAlgebra:

| Name | Description | Documentation | | ---- | ----------- | ------------- | | Bicomplexes | Bicomplexes for Abelian categories | | | ComplexesCategories | Category of (co)chain complexes of an additive category | | | DerivedCategories | Derived categories of Abelian categories | | | HomotopyCategories | Homotopy categories of additive categories | | | StableCategories | Stable categories of additive categories | | | ToolsForHigherHomologicalAlgebra | Tools for the Higher Homological Algebra project | | | TriangulatedCategories | Framework for triangulated categories | |

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Installation

The packages can easily be obtained by cloning the repository HigherHomologicalAlgebra in the pkg directory of the Gap installation.

Required packages

• This package is written to handle categories that are already implemented in CAP, so you will need a fresh version of CAP. You may install it from CAP_project

• You will also need

  • homalg_project
  • CategoricalTowers

• Other needed packages

  • https://github.com/homalg-project/FinSetsForCAP/
  • https://github.com/sunnyquiver/QPA2/

• For the installation of Gap see gap-system-website

License

These packages are free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your opinion) any later version.