# BSc Leon Vatthauer

Here I am formalizing some notions of this paper [https://arxiv.org/pdf/2102.11828.pdf](https://arxiv.org/pdf/2102.11828.pdf) in agda.
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:
```sh
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](https://github.com/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](https://github.com/agda/agda-categories/pull/381)]
    - `Categories.Monad.Construction.Kleisli`
2. Distributive categories (and the relation to extensivity) [[merged](https://github.com/agda/agda-categories/pull/383)] [[merged](https://github.com/agda/agda-categories/pull/410)]
    - `Categories.Category.Distributive`
    - `Categories.Category.Distributive.Properties`
    - `Categories.Category.Extensive.Bundle`
    - `Categories.Category.Extensive.Properties.Distributive`
3. Parametrized (or stable) natural numbers objects [[merged](https://github.com/agda/agda-categories/pull/394)]
    - `Categories.Object.NaturalNumbers.Parametrized`
    - `Categories.Object.NaturalNumbers.Properties.F-Algebra`
    - `Categories.Object.NaturalNumbers.Properties.Parametrized`
4. Commutative monad [[merged](https://github.com/agda/agda-categories/pull/404)]
    - `Categories.Monad.Commutative`
    - `Categories.Monad.Strong.Properties`