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Decide on the kind of functors #2

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omelkonian opened this issue Jan 16, 2024 · 0 comments
Open

Decide on the kind of functors #2

omelkonian opened this issue Jan 16, 2024 · 0 comments
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@omelkonian
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Functors are currently given the type/kind: Type↑ = ∀ {ℓ} → Type ℓ → Type ℓ . This disallows valid cases that the level changes in the output index, so we should carefully decide which ones we want to support + provide alternative definitions to cover the rest.

@WhatisRT has a use case for his axiomatic set-theory library, where one cannot a monad instance for the powerset construction.


Possible alternative definitions:

  • outer quantification: Type↑ a b = Type a → Type b (e.g. covers disjoint union / co-products, but fails for TC)
  • the ultra-general Type↑ f = ∀ {ℓ} → Type ℓ → Type (f ℓ)
  • ...
@omelkonian omelkonian added the question Further information is requested label Jan 16, 2024
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