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# 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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## Running the project
TODO
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## 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) [[**WIP** ](https://github.com/agda/agda-categories/pull/383 )]
- `Categories.Category.Distributive`
- `Categories.Category.Extensive.Bundle`
- `Categories.Category.Extensive.Properties.Distributive`
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## Goals
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- [X] `ElgotAlgebra.agda`
- [X] Formalize (un-)guarded elgot-algebra.
- [X] Show the equivalence of `#-Folding` and `#-Compositionality` in the unguarded case. (*Proposition 10*)
- [ ] `ElgotAlgebras.agda`
- [X] Formalize the category of elgot algebras for a given carrier.
- [X] Show existence of products in this category
- [ ] Show existence of exponentials (if carrier has exponentials)
- [ ] Theorem 37 (final goal)
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## Roadmap
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TODO
## TODOs
- [ ] Create Roadmap (find what theorem 37 depends on and then create a game plan)
- [ ] Refactor `ElgotAlgebras.agda` using `Categories.Morphism.Reasoning` (nicer proofs)