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Prove the five lemma for groups #46

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opened 2024-11-02 19:50:01 +00:00 by michael · 3 comments
michael commented 2024-11-02 19:50:01 +00:00
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Update: Solution at 90f76baca0/src/Misc/FiveLemma/Group/Lemma.agda

  • n is surjective (#47)
  • n is injective (#48)
**Update:** Solution at https://git.mzhang.io/michael/type-theory/src/commit/90f76baca0f22278b8b674aa027389b1a4ae41cb/src/Misc/FiveLemma/Group/Lemma.agda ![](https://upload.wikimedia.org/wikipedia/commons/thumb/f/f8/5_lemma.svg/388px-5_lemma.svg.png) - [x] n is surjective (#47) - [x] n is injective (#48)
michael added this to the research project 2024-11-02 19:50:01 +00:00
michael added a new dependency 2024-11-02 19:50:45 +00:00
#23 Understand and define exact sequences
michael commented 2024-11-05 07:10:52 +00:00
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Very close to the n surjective result, I defined a different definition of isInIm that isn't truncated:

Lines 25 to 26 in e02f49c
isInIm' : GroupHom G H → ⟨ H ⟩ → Type _
isInIm' {G = G} ϕ h = Σ[ g ∈ ⟨ G ⟩ ] ϕ .fst g ≡ h

Very close to the n surjective result, I defined a different definition of `isInIm` that isn't truncated: https://git.mzhang.io/michael/type-theory/src/commit/e02f49c46df6d4583bcc1b92f88d733675afc235/src/Misc/FiveLemma/GroupMorphisms.agda#L25-L26
michael changed title from Prove the five lemma to Prove the five lemma for groups 2024-11-05 07:20:02 +00:00
michael commented 2024-11-05 07:20:18 +00:00
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Changing this issue to specifically be about groups, will add another one for categories later

Changing this issue to specifically be about groups, will add another one for categories later
michael commented 2024-11-05 09:26:08 +00:00
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Done! See 90f76baca0/src/Misc/FiveLemma/Group/Lemma.agda for solution

Done! See https://git.mzhang.io/michael/type-theory/src/commit/90f76baca0f22278b8b674aa027389b1a4ae41cb/src/Misc/FiveLemma/Group/Lemma.agda for solution
michael removed a dependency 2024-11-05 09:26:20 +00:00
#23 Understand and define exact sequences
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