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38 lines
2.1 KiB
Markdown
38 lines
2.1 KiB
Markdown
# BSc Leon Vatthauer
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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.
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The whole project consists of literate agda files, where I add my documentation as markdown.
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A (mostly up to date) version can be found here: https://wwwcip.cs.fau.de/~hy84coky/bsc-thesis/
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## Usage
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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.
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To use the project you just have to open a development shell:
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```sh
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nix develop .
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```
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(this will take 20 - 30 minutes the first time, because it has to typecheck the agda-categories library)
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There is also a Makefile for compiling every module and generating the html documentation.
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```
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make
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```
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## Contributions to *agda-categories*
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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.
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So far the contributions are:
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1. Kleisli triples [[merged](https://github.com/agda/agda-categories/pull/381)]
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- `Categories.Monad.Construction.Kleisli`
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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)]
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- `Categories.Category.Distributive`
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- `Categories.Category.Distributive.Properties`
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- `Categories.Category.Extensive.Bundle`
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- `Categories.Category.Extensive.Properties.Distributive`
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3. Parametrized (or stable) natural numbers objects [[merged](https://github.com/agda/agda-categories/pull/394)]
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- `Categories.Object.NaturalNumbers.Parametrized`
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- `Categories.Object.NaturalNumbers.Properties.F-Algebra`
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- `Categories.Object.NaturalNumbers.Properties.Parametrized`
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4. Commutative monad [[merged](https://github.com/agda/agda-categories/pull/404)]
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- `Categories.Monad.Commutative`
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- `Categories.Monad.Strong.Properties`
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