2018-02-21 13:06:09 +00:00
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Backlog
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=======
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2018-03-13 10:29:13 +00:00
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Prove postulates in `Cat.Wishlist`:
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* `ntypeCommulative : n ≤ m → HasLevel ⟨ n ⟩₋₂ A → HasLevel ⟨ m ⟩₋₂ A`
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2018-03-07 23:54:42 +00:00
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Prove univalence for the category of
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2018-03-13 10:29:13 +00:00
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* the opposite category
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2018-03-07 23:54:42 +00:00
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* sets
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2018-03-13 10:29:13 +00:00
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This does not follow trivially from `Cubical.Univalence.univalence` because
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objects are not `Set` but `hSet`
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2018-03-07 23:54:42 +00:00
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* functors and natural transformations
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2018-02-24 13:00:52 +00:00
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2018-03-08 00:09:40 +00:00
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Prove:
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* `isProp (Product ...)`
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* `isProp (HasProducts ...)`
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2018-02-24 13:00:52 +00:00
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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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2018-03-07 23:54:42 +00:00
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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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2018-03-13 10:29:13 +00:00
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* Kleisli ≃ Monoidal ✓
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* Problem 2.3 in [voe]
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2018-03-07 23:54:42 +00:00
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* 1st contruction ~ monoidal ✓
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* 2nd contruction ~ klesli ✓
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* 1st ≃ 2nd ✗
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2018-03-13 10:29:13 +00:00
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I've managed to set this up so I should be able to reuse the proof that
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Kleisli ≃ Monoidal, but I don't know why it doesn't typecheck.
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