44 lines
1.2 KiB
Markdown
44 lines
1.2 KiB
Markdown
Backlog
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=======
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Prove univalence for the category of
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* functors and natural transformations
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In AreInverses, dont use the "point-free" version. I.e.:
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`∀ x → f x ≡ g x` rather than `f ≡ g`
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Ideas for future work
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---------------------
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It would be nice if my formulation of monads is not so "stand-alone" as it is at
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the moment.
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We can built up the notion of monads and related concept in multiple ways as
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demonstrated in the two equivalent formulations of monads (kleisli/monoidal):
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There seems to be a category-theoretic approach and an approach more in the
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style of functional programming as e.g. the related typeclasses in the
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standard library of Haskell.
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It would be nice to build up this hierarchy in two ways: The
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"category-theoretic" way and the "functional programming" way.
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Here is an overview of some of the concepts that need to be developed to acheive
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this:
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* Functor ✓
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* Applicative Functor ✗
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* Lax monoidal functor ✗
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* Monoidal functor ✗
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* Tensorial strength ✗
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* Category ✓
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* Monoidal category ✗
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* Monad
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* Monoidal monad ✓
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* Kleisli monad ✓
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* Kleisli ≃ Monoidal ✓
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* Problem 2.3 in [voe] ✓
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* 1st contruction ~ monoidal ✓
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* 2nd contruction ~ klesli ✓
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* 1st ≃ 2nd ✓
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