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README.md

BSc Leon Vatthauer

Here I am formalizing some notions of this paper 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/

Running the project

TODO

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]
    • Categories.Category.Distributive
    • 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 [TODO]

TODO

TODOs are found inside the literate agda files!

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