[Merged by Bors] - feat(category_theory/limits): The associativity of pullbacks and pushouts. #10619
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jcommelin
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| /-- | ||
| Given | ||
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| X₁ - f₁ -> X₂ - f₂ -> X₃ | ||
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| i₁ i₂ i₃ | ||
| ∨ ∨ ∨ | ||
| Y₁ - g₁ -> Y₂ - g₂ -> Y₃ | ||
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| Then the big square is a pullback if both the small squares are. | ||
| -/ |
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What happens if we stack the squares vertically? It's math-trivial that a similar statement holds. But it's not Lean defeq, I guess. Can we avoid duplication?
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Composing with either pullback_symmetry or pullback_cone.flip_is_pullback works.
I'm not sure if there are better ways to do so.
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I hope that will be good enough in practice.
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Dec 13, 2021
…outs. (#10619) Also provides the pasting lemma for pullback (pushout) squares Co-authored-by: erd1 <the.erd.one@gmail.com>
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Also provides the pasting lemma for pullback (pushout) squares