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Refactor the 'Categories.Object.Zero' module #252

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merged 3 commits into from
Feb 23, 2021

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TOTBWF
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@TOTBWF TOTBWF commented Feb 23, 2021

As per @HuStmpHrrr's suggestion on #249, I've reworked the definition of zero objects to use IsTerminal and IsInitial. I also made a couple of fixes to some rather silly mistakes I made when writing this module:

  • I've added a predicate version of Zero
  • I've renamed zero to 𝟘, to avoid conflicts with zero from Level, Data.Nat, and many others!
  • I've flipped ¡ and ! so that their types now make sense:
    ¡ : 𝟘 ⇒ A
    ! : A ⇒ 𝟘

While I was at it, I added some autoduality proofs about zero objects that I need for cokernels.

@HuStmpHrrr
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Wonderful. That's very cool.

@JacquesCarette JacquesCarette merged commit 1c49991 into agda:master Feb 23, 2021
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4 participants