[Merged by Bors] - feat(topology/category/*/projective): CompHaus and Profinite have enough projectives #8613
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Aug 10, 2021
| @@ -169,23 +170,27 @@ def limit_cone {J : Type u} [small_category J] (F : J ⥤ CompHaus.{u}) : | |||
| { X := | |||
| { to_Top := (Top.limit_cone (F ⋙ CompHaus_to_Top)).X, | |||
| is_compact := begin | |||
| dsimp [Top.limit_cone], | |||
| show compact_space ↥{u : Π j, (F.obj j) | ∀ {i j : J} (f : i ⟶ j), (F.map f) (u i) = u j}, | |||
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All the changes to this proof are merely to speed it up so that it doesn't time out in my VScode.
semorrison
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Aug 12, 2021
semorrison
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Aug 12, 2021
semorrison
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Aug 12, 2021
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Could we add a reference to an informal proof of these facts? Chapter 21 of https://www.google.com.au/books/edition/_/w6or65-Hw6UC?hl=en&gbpv=0 has CompHaus has enough projectives. |
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Otherwise, looks great! |
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I've added a reference. |
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bors merge |
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Aug 16, 2021
…ugh projectives (#8613) Co-authored-by: Adam Topaz <github@adamtopaz.com> Co-authored-by: Adam Topaz <github@adamtopaz.com>
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Pull request successfully merged into master. Build succeeded: |
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Co-authored-by: Adam Topaz github@adamtopaz.com