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

CAP project -- Categories, Algorithms, and Programming
https://github.com/homalg-project/cap_project
additive-closure adelman-category category-theory freyd-category homological-algebra internalization modules vector-spaces
Last synced: 3 months ago
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CAP project -- Categories, Algorithms, and Programming
Host: GitHub
URL: https://github.com/homalg-project/cap_project
Owner: homalg-project
Created: 2015-04-10T08:52:40.000Z (about 10 years ago)
Default Branch: master
Last Pushed: 2025-03-01T10:48:40.000Z (3 months ago)
Last Synced: 2025-03-01T11:27:21.596Z (3 months ago)
Topics: additive-closure, adelman-category, category-theory, freyd-category, homological-algebra, internalization, modules, vector-spaces
Language: GAP
Homepage: https://homalg-project.github.io/docs/CAP_project-based/
Size: 49.6 MB
Stars: 25
Watchers: 8
Forks: 18
Open Issues: 89
Metadata Files:
- Readme: README.md
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README

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

### Categories, Algorithms, and Programming

| Build Status | Code Coverage |

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

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

Welcome to the CAP project.

This repository contains the GAP package [CAP](CAP#readme) and many packages based on it (see the [table below](#packages-of-cap_project)). For more packages based on CAP which are not part of this repository, see the table on [this page](https://homalg-project.github.io/docs/CAP_project-based/).

## Manual

Please take a look at our [manual](https://github.com/homalg-project/CAP_project/raw/master/Manual/CAPManual.pdf) for a first introduction to CAP.

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

| Name | Description | Documentation |

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

| [CAP](CAP#readme) | Categories, Algorithms, Programming | [![HTML stable documentation][html-CAP-img]][html-CAP-url] [![PDF stable documentation][pdf-CAP-img]][pdf-CAP-url] |

| [ActionsForCAP](ActionsForCAP#readme) | Actions and Coactions for CAP | [![HTML stable documentation][html-ActionsForCAP-img]][html-ActionsForCAP-url] [![PDF stable documentation][pdf-ActionsForCAP-img]][pdf-ActionsForCAP-url] |

| [AttributeCategoryForCAP](AttributeCategoryForCAP#readme) | Automatic enhancement with attributes of a CAP category | [![HTML stable documentation][html-AttributeCategoryForCAP-img]][html-AttributeCategoryForCAP-url] [![PDF stable documentation][pdf-AttributeCategoryForCAP-img]][pdf-AttributeCategoryForCAP-url] |

| [CartesianCategories](CartesianCategories#readme) | Cartesian and cocartesian categories and various subdoctrines | [![HTML stable documentation][html-CartesianCategories-img]][html-CartesianCategories-url] [![PDF stable documentation][pdf-CartesianCategories-img]][pdf-CartesianCategories-url] |

| [CompilerForCAP](CompilerForCAP#readme) | Speed up and verify categorical algorithms | [![HTML stable documentation][html-CompilerForCAP-img]][html-CompilerForCAP-url] [![PDF stable documentation][pdf-CompilerForCAP-img]][pdf-CompilerForCAP-url] |

| [ComplexesAndFilteredObjectsForCAP](ComplexesAndFilteredObjectsForCAP#readme) | Implementation of complexes, cocomplexes and filtered objects for CAP | [![HTML stable documentation][html-ComplexesAndFilteredObjectsForCAP-img]][html-ComplexesAndFilteredObjectsForCAP-url] [![PDF stable documentation][pdf-ComplexesAndFilteredObjectsForCAP-img]][pdf-ComplexesAndFilteredObjectsForCAP-url] |

| [FreydCategoriesForCAP](FreydCategoriesForCAP#readme) | Freyd categories - Formal (co)kernels for additive categories | [![HTML stable documentation][html-FreydCategoriesForCAP-img]][html-FreydCategoriesForCAP-url] [![PDF stable documentation][pdf-FreydCategoriesForCAP-img]][pdf-FreydCategoriesForCAP-url] |

| [GeneralizedMorphismsForCAP](GeneralizedMorphismsForCAP#readme) | Implementations of generalized morphisms for the CAP project | [![HTML stable documentation][html-GeneralizedMorphismsForCAP-img]][html-GeneralizedMorphismsForCAP-url] [![PDF stable documentation][pdf-GeneralizedMorphismsForCAP-img]][pdf-GeneralizedMorphismsForCAP-url] |

| [GradedModulePresentationsForCAP](GradedModulePresentationsForCAP#readme) | Presentations for graded modules | [![HTML stable documentation][html-GradedModulePresentationsForCAP-img]][html-GradedModulePresentationsForCAP-url] [![PDF stable documentation][pdf-GradedModulePresentationsForCAP-img]][pdf-GradedModulePresentationsForCAP-url] |

| [GroupRepresentationsForCAP](GroupRepresentationsForCAP#readme) | Skeletal category of group representations for CAP | [![HTML stable documentation][html-GroupRepresentationsForCAP-img]][html-GroupRepresentationsForCAP-url] [![PDF stable documentation][pdf-GroupRepresentationsForCAP-img]][pdf-GroupRepresentationsForCAP-url] |

| [HomologicalAlgebraForCAP](HomologicalAlgebraForCAP#readme) | Homological algebra algorithms for CAP | [![HTML stable documentation][html-HomologicalAlgebraForCAP-img]][html-HomologicalAlgebraForCAP-url] [![PDF stable documentation][pdf-HomologicalAlgebraForCAP-img]][pdf-HomologicalAlgebraForCAP-url] |

| [InternalExteriorAlgebraForCAP](InternalExteriorAlgebraForCAP#readme) | Constructions for Modules over the Internal Exterior Algebra for CAP | [![HTML stable documentation][html-InternalExteriorAlgebraForCAP-img]][html-InternalExteriorAlgebraForCAP-url] [![PDF stable documentation][pdf-InternalExteriorAlgebraForCAP-img]][pdf-InternalExteriorAlgebraForCAP-url] |

| [LinearAlgebraForCAP](LinearAlgebraForCAP#readme) | Category of Matrices over a Field for CAP | [![HTML stable documentation][html-LinearAlgebraForCAP-img]][html-LinearAlgebraForCAP-url] [![PDF stable documentation][pdf-LinearAlgebraForCAP-img]][pdf-LinearAlgebraForCAP-url] |

| [ModulePresentationsForCAP](ModulePresentationsForCAP#readme) | Category R-pres for CAP | [![HTML stable documentation][html-ModulePresentationsForCAP-img]][html-ModulePresentationsForCAP-url] [![PDF stable documentation][pdf-ModulePresentationsForCAP-img]][pdf-ModulePresentationsForCAP-url] |

| [ModulesOverLocalRingsForCAP](ModulesOverLocalRingsForCAP#readme) | Category of modules over a local ring modeled by Serre quotients for CAP | [![HTML stable documentation][html-ModulesOverLocalRingsForCAP-img]][html-ModulesOverLocalRingsForCAP-url] [![PDF stable documentation][pdf-ModulesOverLocalRingsForCAP-img]][pdf-ModulesOverLocalRingsForCAP-url] |

| [MonoidalCategories](MonoidalCategories#readme) | Monoidal and monoidal (co)closed categories | [![HTML stable documentation][html-MonoidalCategories-img]][html-MonoidalCategories-url] [![PDF stable documentation][pdf-MonoidalCategories-img]][pdf-MonoidalCategories-url] |

| [ToricSheaves](ToricSheaves#readme) | Toric sheaves as Serre quotients | [![HTML stable documentation][html-ToricSheaves-img]][html-ToricSheaves-url] [![PDF stable documentation][pdf-ToricSheaves-img]][pdf-ToricSheaves-url] |

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

[html-CAP-url]: https://homalg-project.github.io/CAP_project/CAP/doc/chap0_mj.html

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

[pdf-CAP-url]: https://homalg-project.github.io/CAP_project/CAP/download_pdf.html

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

[html-ActionsForCAP-url]: https://homalg-project.github.io/CAP_project/ActionsForCAP/doc/chap0_mj.html

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

[pdf-ActionsForCAP-url]: https://homalg-project.github.io/CAP_project/ActionsForCAP/download_pdf.html

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

[html-AttributeCategoryForCAP-url]: https://homalg-project.github.io/CAP_project/AttributeCategoryForCAP/doc/chap0_mj.html

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

[pdf-AttributeCategoryForCAP-url]: https://homalg-project.github.io/CAP_project/AttributeCategoryForCAP/download_pdf.html

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

[html-CartesianCategories-url]: https://homalg-project.github.io/CAP_project/CartesianCategories/doc/chap0_mj.html

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

[pdf-CartesianCategories-url]: https://homalg-project.github.io/CAP_project/CartesianCategories/download_pdf.html

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

[html-CompilerForCAP-url]: https://homalg-project.github.io/CAP_project/CompilerForCAP/doc/chap0_mj.html

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

[pdf-CompilerForCAP-url]: https://homalg-project.github.io/CAP_project/CompilerForCAP/download_pdf.html

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

[html-ComplexesAndFilteredObjectsForCAP-url]: https://homalg-project.github.io/CAP_project/ComplexesAndFilteredObjectsForCAP/doc/chap0_mj.html

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

[pdf-ComplexesAndFilteredObjectsForCAP-url]: https://homalg-project.github.io/CAP_project/ComplexesAndFilteredObjectsForCAP/download_pdf.html

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

[html-FreydCategoriesForCAP-url]: https://homalg-project.github.io/CAP_project/FreydCategoriesForCAP/doc/chap0_mj.html

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

[pdf-FreydCategoriesForCAP-url]: https://homalg-project.github.io/CAP_project/FreydCategoriesForCAP/download_pdf.html

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

[html-GeneralizedMorphismsForCAP-url]: https://homalg-project.github.io/CAP_project/GeneralizedMorphismsForCAP/doc/chap0_mj.html

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

[pdf-GeneralizedMorphismsForCAP-url]: https://homalg-project.github.io/CAP_project/GeneralizedMorphismsForCAP/download_pdf.html

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

[html-GradedModulePresentationsForCAP-url]: https://homalg-project.github.io/CAP_project/GradedModulePresentationsForCAP/doc/chap0_mj.html

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

[pdf-GradedModulePresentationsForCAP-url]: https://homalg-project.github.io/CAP_project/GradedModulePresentationsForCAP/download_pdf.html

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

[html-GroupRepresentationsForCAP-url]: https://homalg-project.github.io/CAP_project/GroupRepresentationsForCAP/doc/chap0_mj.html

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

[pdf-GroupRepresentationsForCAP-url]: https://homalg-project.github.io/CAP_project/GroupRepresentationsForCAP/download_pdf.html

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

[html-HomologicalAlgebraForCAP-url]: https://homalg-project.github.io/CAP_project/HomologicalAlgebraForCAP/doc/chap0_mj.html

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

[pdf-HomologicalAlgebraForCAP-url]: https://homalg-project.github.io/CAP_project/HomologicalAlgebraForCAP/download_pdf.html

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

[html-InternalExteriorAlgebraForCAP-url]: https://homalg-project.github.io/CAP_project/InternalExteriorAlgebraForCAP/doc/chap0_mj.html

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

[pdf-InternalExteriorAlgebraForCAP-url]: https://homalg-project.github.io/CAP_project/InternalExteriorAlgebraForCAP/download_pdf.html

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

[html-LinearAlgebraForCAP-url]: https://homalg-project.github.io/CAP_project/LinearAlgebraForCAP/doc/chap0_mj.html

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

[pdf-LinearAlgebraForCAP-url]: https://homalg-project.github.io/CAP_project/LinearAlgebraForCAP/download_pdf.html

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

[html-ModulePresentationsForCAP-url]: https://homalg-project.github.io/CAP_project/ModulePresentationsForCAP/doc/chap0_mj.html

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

[pdf-ModulePresentationsForCAP-url]: https://homalg-project.github.io/CAP_project/ModulePresentationsForCAP/download_pdf.html

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

[html-ModulesOverLocalRingsForCAP-url]: https://homalg-project.github.io/CAP_project/ModulesOverLocalRingsForCAP/doc/chap0_mj.html

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

[pdf-ModulesOverLocalRingsForCAP-url]: https://homalg-project.github.io/CAP_project/ModulesOverLocalRingsForCAP/download_pdf.html

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

[html-MonoidalCategories-url]: https://homalg-project.github.io/CAP_project/MonoidalCategories/doc/chap0_mj.html

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

[pdf-MonoidalCategories-url]: https://homalg-project.github.io/CAP_project/MonoidalCategories/download_pdf.html

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

[html-ToricSheaves-url]: https://homalg-project.github.io/CAP_project/ToricSheaves/doc/chap0_mj.html

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

[pdf-ToricSheaves-url]: https://homalg-project.github.io/CAP_project/ToricSheaves/download_pdf.html

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

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

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

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

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

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