[Merged by Bors] - feat: two homotopic maps of short complexes induce the same map in homology #8079
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joelriou
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Nov 1, 2023
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joelriou
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jcommelin
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Nov 1, 2023
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| lemma congr_leftHomologyMap' (h : Homotopy φ₁ φ₂) (h₁ : S₁.LeftHomologyData) | ||
| (h₂ : S₂.LeftHomologyData) : leftHomologyMap' φ₁ h₁ h₂ = leftHomologyMap' φ₂ h₁ h₂ := by | ||
| rw [h.eq_add_nullHomotopic, leftHomologyMap'_add, leftHomologyMap'_nullHomotopic, add_zero] | ||
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| lemma congr_rightHomologyMap' (h : Homotopy φ₁ φ₂) (h₁ : S₁.RightHomologyData) | ||
| (h₂ : S₂.RightHomologyData) : rightHomologyMap' φ₁ h₁ h₂ = rightHomologyMap' φ₂ h₁ h₂ := by | ||
| rw [h.eq_add_nullHomotopic, rightHomologyMap'_add, rightHomologyMap'_nullHomotopic, add_zero] | ||
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| lemma congr_homologyMap' (h : Homotopy φ₁ φ₂) (h₁ : S₁.HomologyData) | ||
| (h₂ : S₂.HomologyData) : homologyMap' φ₁ h₁ h₂ = homologyMap' φ₂ h₁ h₂ := by | ||
| rw [h.eq_add_nullHomotopic, homologyMap'_add, homologyMap'_nullHomotopic, add_zero] | ||
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| lemma congr_leftHomologyMap (h : Homotopy φ₁ φ₂) [S₁.HasLeftHomology] [S₂.HasLeftHomology] : | ||
| leftHomologyMap φ₁ = leftHomologyMap φ₂ := | ||
| h.congr_leftHomologyMap' _ _ | ||
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| lemma congr_rightHomologyMap (h : Homotopy φ₁ φ₂) [S₁.HasRightHomology] [S₂.HasRightHomology] : | ||
| rightHomologyMap φ₁ = rightHomologyMap φ₂ := | ||
| h.congr_rightHomologyMap' _ _ | ||
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| lemma congr_homologyMap (h : Homotopy φ₁ φ₂) [S₁.HasHomology] [S₂.HasHomology] : | ||
| homologyMap φ₁ = homologyMap φ₂ := | ||
| h.congr_homologyMap' _ _ |
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I think I would put the congr at the end of the name, instead of at the start. I feel like that way there also a bigger chance of discovering it via autocompletion when searching for names about leftHomologyMap etc...
What do you think?
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Thanks for the suggestion. I have made congr a suffix here.
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