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https://github.com/homalg-project/higherhomologicalalgebra

A GAP framework for categorical homological algebra with special focus on homotopy categories and tilting equivalences
https://github.com/homalg-project/higherhomologicalalgebra

complex-categories derived-category derived-equivalences gap homological-algebra homotopy-category triangulated-categories

Last synced: about 2 months ago
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A GAP framework for categorical homological algebra with special focus on homotopy categories and tilting equivalences

Host: GitHub
URL: https://github.com/homalg-project/higherhomologicalalgebra
Owner: homalg-project
Created: 2020-08-10T22:37:55.000Z (over 4 years ago)
Default Branch: master
Last Pushed: 2024-09-14T04:21:26.000Z (4 months ago)
Last Synced: 2024-09-14T22:32:12.918Z (4 months ago)
Topics: complex-categories, derived-category, derived-equivalences, gap, homological-algebra, homotopy-category, triangulated-categories
Language: GAP
Homepage: https://homalg-project.github.io/HigherHomologicalAlgebra
Size: 6.68 MB
Stars: 5
Watchers: 5
Forks: 6
Open Issues: 3
Metadata Files:
- Readme: README.md

Awesome Lists containing this project

README

        
# HigherHomologicalAlgebra ^{^{[![View code][code-img]][code-url]}}

### Higher Homological Algebra

| Build Status | Code Coverage |

| ------------ | ------------- |

| [![Build Status][tests-img]][tests-url] | [![Code Coverage][codecov-img]][codecov-url] |

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.

### Packages of [HigherHomologicalAlgebra](/../../):

| Name | Description | Documentation |

| ---- | ----------- | ------------- |

| [Bicomplexes](Bicomplexes#readme) | Bicomplexes for Abelian categories | [![HTML stable documentation][html-Bicomplexes-img]][html-Bicomplexes-url] [![PDF stable documentation][pdf-Bicomplexes-img]][pdf-Bicomplexes-url] |

| [ComplexesCategories](ComplexesCategories#readme) | Category of (co)chain complexes of an additive category | [![HTML stable documentation][html-ComplexesCategories-img]][html-ComplexesCategories-url] [![PDF stable documentation][pdf-ComplexesCategories-img]][pdf-ComplexesCategories-url] |

| [DerivedCategories](DerivedCategories#readme) | Derived categories of Abelian categories | [![HTML stable documentation][html-DerivedCategories-img]][html-DerivedCategories-url] [![PDF stable documentation][pdf-DerivedCategories-img]][pdf-DerivedCategories-url] |

| [HomotopyCategories](HomotopyCategories#readme) | Homotopy categories of additive categories | [![HTML stable documentation][html-HomotopyCategories-img]][html-HomotopyCategories-url] [![PDF stable documentation][pdf-HomotopyCategories-img]][pdf-HomotopyCategories-url] |

| [StableCategories](StableCategories#readme) | Stable categories of additive categories | [![HTML stable documentation][html-StableCategories-img]][html-StableCategories-url] [![PDF stable documentation][pdf-StableCategories-img]][pdf-StableCategories-url] |

| [ToolsForHigherHomologicalAlgebra](ToolsForHigherHomologicalAlgebra#readme) | Tools for the Higher Homological Algebra project | [![HTML stable documentation][html-ToolsForHigherHomologicalAlgebra-img]][html-ToolsForHigherHomologicalAlgebra-url] [![PDF stable documentation][pdf-ToolsForHigherHomologicalAlgebra-img]][pdf-ToolsForHigherHomologicalAlgebra-url] |

| [TriangulatedCategories](TriangulatedCategories#readme) | Framework for triangulated categories | [![HTML stable documentation][html-TriangulatedCategories-img]][html-TriangulatedCategories-url] [![PDF stable documentation][pdf-TriangulatedCategories-img]][pdf-TriangulatedCategories-url] |

[html-Bicomplexes-img]: https://img.shields.io/badge/🔗%20HTML-stable-blue.svg

[html-Bicomplexes-url]: https://homalg-project.github.io/HigherHomologicalAlgebra/Bicomplexes/doc/chap0_mj.html

[pdf-Bicomplexes-img]: https://img.shields.io/badge/🔗%20PDF-stable-blue.svg

[pdf-Bicomplexes-url]: https://homalg-project.github.io/HigherHomologicalAlgebra/Bicomplexes/download_pdf.html

[html-ComplexesCategories-img]: https://img.shields.io/badge/🔗%20HTML-stable-blue.svg

[html-ComplexesCategories-url]: https://homalg-project.github.io/HigherHomologicalAlgebra/ComplexesCategories/doc/chap0_mj.html

[pdf-ComplexesCategories-img]: https://img.shields.io/badge/🔗%20PDF-stable-blue.svg

[pdf-ComplexesCategories-url]: https://homalg-project.github.io/HigherHomologicalAlgebra/ComplexesCategories/download_pdf.html

[html-DerivedCategories-img]: https://img.shields.io/badge/🔗%20HTML-stable-blue.svg

[html-DerivedCategories-url]: https://homalg-project.github.io/HigherHomologicalAlgebra/DerivedCategories/doc/chap0_mj.html

[pdf-DerivedCategories-img]: https://img.shields.io/badge/🔗%20PDF-stable-blue.svg

[pdf-DerivedCategories-url]: https://homalg-project.github.io/HigherHomologicalAlgebra/DerivedCategories/download_pdf.html

[html-HomotopyCategories-img]: https://img.shields.io/badge/🔗%20HTML-stable-blue.svg

[html-HomotopyCategories-url]: https://homalg-project.github.io/HigherHomologicalAlgebra/HomotopyCategories/doc/chap0_mj.html

[pdf-HomotopyCategories-img]: https://img.shields.io/badge/🔗%20PDF-stable-blue.svg

[pdf-HomotopyCategories-url]: https://homalg-project.github.io/HigherHomologicalAlgebra/HomotopyCategories/download_pdf.html

[html-StableCategories-img]: https://img.shields.io/badge/🔗%20HTML-stable-blue.svg

[html-StableCategories-url]: https://homalg-project.github.io/HigherHomologicalAlgebra/StableCategories/doc/chap0_mj.html

[pdf-StableCategories-img]: https://img.shields.io/badge/🔗%20PDF-stable-blue.svg

[pdf-StableCategories-url]: https://homalg-project.github.io/HigherHomologicalAlgebra/StableCategories/download_pdf.html

[html-ToolsForHigherHomologicalAlgebra-img]: https://img.shields.io/badge/🔗%20HTML-stable-blue.svg

[html-ToolsForHigherHomologicalAlgebra-url]: https://homalg-project.github.io/HigherHomologicalAlgebra/ToolsForHigherHomologicalAlgebra/doc/chap0_mj.html

[pdf-ToolsForHigherHomologicalAlgebra-img]: https://img.shields.io/badge/🔗%20PDF-stable-blue.svg

[pdf-ToolsForHigherHomologicalAlgebra-url]: https://homalg-project.github.io/HigherHomologicalAlgebra/ToolsForHigherHomologicalAlgebra/download_pdf.html

[html-TriangulatedCategories-img]: https://img.shields.io/badge/🔗%20HTML-stable-blue.svg

[html-TriangulatedCategories-url]: https://homalg-project.github.io/HigherHomologicalAlgebra/TriangulatedCategories/doc/chap0_mj.html

[pdf-TriangulatedCategories-img]: https://img.shields.io/badge/🔗%20PDF-stable-blue.svg

[pdf-TriangulatedCategories-url]: https://homalg-project.github.io/HigherHomologicalAlgebra/TriangulatedCategories/download_pdf.html

[tests-img]: https://github.com/homalg-project/HigherHomologicalAlgebra/actions/workflows/Tests.yml/badge.svg?branch=master

[tests-url]: https://github.com/homalg-project/HigherHomologicalAlgebra/actions/workflows/Tests.yml?query=branch%3Amaster

[codecov-img]: https://codecov.io/gh/homalg-project/HigherHomologicalAlgebra/branch/master/graph/badge.svg

[codecov-url]: https://app.codecov.io/gh/homalg-project/HigherHomologicalAlgebra

[code-img]: https://img.shields.io/badge/-View%20code-blue?logo=github

[code-url]: https://github.com/homalg-project/HigherHomologicalAlgebra#top

Installation

-----------

The packages can easily be obtained by cloning the repository

[HigherHomologicalAlgebra](https://github.com/homalg-project/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](https://github.com/homalg-project/CAP_project)

* You will also need

  - [homalg_project](https://github.com/homalg-project/homalg_project.git)

  - [CategoricalTowers](https://github.com/homalg-project/CategoricalTowers.git)

* Other needed packages

  - https://github.com/homalg-project/FinSetsForCAP/

  - https://github.com/sunnyquiver/QPA2/

 

* For the installation of Gap see [gap-system-website](https://www.gap-system.org)

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.