bsc-leon-vatthauer/agda

The Agda formalization

The whole project consists of literate agda files, where I add my documentation as markdown. A (mostly up to date) version can be found here: https://wwwcip.cs.fau.de/~hy84coky/bsc-thesis/

Usage

The project requires a new version of agda-categories (newer than some package managers ship), so the easiest way to use this project is via the provided nix flake, which fetches my fork of agda-categories that is guaranteed to work with this project.

To use the project you just have to open a development shell:

nix develop .

(this will take 20 - 30 minutes the first time, because it has to typecheck the agda-categories library)

There is also a Makefile for compiling every module and generating the html documentation.

make

Contributions to agda-categories

This project uses the awesome category theory library for agda (agda-categories), it is already very extensive, but some notions needed here are missing, so I contribute them to the library. So far the contributions are:

1. Kleisli triples [merged]
   • Categories.Monad.Construction.Kleisli
2. Distributive categories (and the relation to extensivity) [merged] [merged]
   • Categories.Category.Distributive
   • Categories.Category.Distributive.Properties
   • Categories.Category.Extensive.Bundle
   • Categories.Category.Extensive.Properties.Distributive
3. Parametrized (or stable) natural numbers objects [merged]
   • Categories.Object.NaturalNumbers.Parametrized
   • Categories.Object.NaturalNumbers.Properties.F-Algebra
   • Categories.Object.NaturalNumbers.Properties.Parametrized
4. Commutative monad [merged]
   • Categories.Monad.Commutative
   • Categories.Monad.Strong.Properties