[Merged by Bors] - feat(CategoryTheory): naturality of the connecting homomorphism of the snake lemma#8490
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[Merged by Bors] - feat(CategoryTheory): naturality of the connecting homomorphism of the snake lemma#8490
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| `L₀.X₁ ⟶ L₀.X₂ ⟶ L₀.X₃ ⟶ L₃.X₁ ⟶ L₃.X₂ ⟶ L₃.X₃`. Each of the four exactness | ||
| statement is first stated separately as lemmas `L₀_exact`, `L₁'_exact`, | ||
| `L₂'_exact` and `L₃_exact` and the full 6-term exact sequence is stated | ||
| as `snake_lemma`. This sequence can even be extended with an extra `0` | ||
| on the left (see `mono_L₀_f`) if `L₁.X₁ ⟶ L₁.X₂` is a mono (i.e. `L₁` is short exact), |
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| `L₀.X₁ ⟶ L₀.X₂ ⟶ L₀.X₃ ⟶ L₃.X₁ ⟶ L₃.X₂ ⟶ L₃.X₃`. Each of the four exactness | |
| statement is first stated separately as lemmas `L₀_exact`, `L₁'_exact`, | |
| `L₂'_exact` and `L₃_exact` and the full 6-term exact sequence is stated | |
| as `snake_lemma`. This sequence can even be extended with an extra `0` | |
| on the left (see `mono_L₀_f`) if `L₁.X₁ ⟶ L₁.X₂` is a mono (i.e. `L₁` is short exact), | |
| `L₀.X₁ ⟶ L₀.X₂ ⟶ L₀.X₃ ⟶ L₃.X₁ ⟶ L₃.X₂ ⟶ L₃.X₃`. Each of the four exactness | |
| statements is first stated separately as lemma `L₀_exact`, `L₁'_exact`, | |
| `L₂'_exact` and `L₃_exact` and the full 6-term exact sequence is stated | |
| as `snake_lemma`. This sequence can even be extended with an extra `0` | |
| on the left (see `mono_L₀_f`) if `L₁.X₁ ⟶ L₁.X₂` is a mono (i.e. `L₁` is short exact), |
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…e snake lemma (#8490) In this PR, it is shown that the connecting homomorphism of the snake lemma is natural.
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…e snake lemma (#8490) In this PR, it is shown that the connecting homomorphism of the snake lemma is natural.
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In this PR, it is shown that the connecting homomorphism of the snake lemma is natural.