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A GAP framework for categorical homological algebra with special focus on homotopy categories and tilting equivalences

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HigherHomologicalAlgebra View code

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.

Name Description Documentation
BBGG Beilinson monads and derived categories for coherent sheaves over P^n HTML stable documentation PDF stable documentation
Bicomplexes Bicomplexes for Abelian categories HTML stable documentation PDF stable documentation
ComplexesCategories Category of (co)chain complexes of an additive category HTML stable documentation PDF stable documentation
DerivedCategories Derived categories of Abelian categories HTML stable documentation PDF stable documentation
HomotopyCategories Homotopy categories of additive categories HTML stable documentation PDF stable documentation
QuotientCategories Quotient categories of CAP categories by two-sided ideals HTML stable documentation PDF stable documentation
StableCategories Stable categories of additive categories HTML stable documentation PDF stable documentation
ToolsForHigherHomologicalAlgebra Tools for the Higher Homological Algebra project HTML stable documentation PDF stable documentation
TriangulatedCategories Framework for triangulated categories HTML stable documentation PDF stable documentation

Installation

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

Required packages

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.

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A GAP framework for categorical homological algebra with special focus on homotopy categories and tilting equivalences

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