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Theorems · Theorem · category theory

CategoryTheory.ShortComplex.SnakeInput.snake_lemma

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Abelian C]
  (S : CategoryTheory.ShortComplex.SnakeInput C), S.composableArrows.Exact

The diagram S.L₀.X₁ ⟶ S.L₀.X₂ ⟶ S.L₀.X₃ ⟶ S.L₃.X₁ ⟶ S.L₃.X₂ ⟶ S.L₃.X₃ is exact for any S : SnakeInput C.

Defined in
Mathlib.Algebra.Homology.ShortComplex.SnakeLemma
Cited by
1 results in Mathlib
Foundations
Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Abelian
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CategoryTheory.kernelCokernelCompSequence_exact · cited by 0CategoryTheory.kernelCoke…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianCategoryTheory.ShortComplex.SnakeInput · cited by 129ShortComplex.SnakeInputCategoryTheory.ComposableArrows.Exact · cited by 65ComposableArrows.ExactCategoryTheory.ShortComplex.Exact.exact_toComposableArrows · cited by 20Exact.exact_toComposableA…CategoryTheory.ComposableArrows.exact_of_δ₀ · cited by 10ComposableArrows.exact_of…CategoryTheory.ShortComplex.SnakeInput.L₁'_exact · cited by 4SnakeInput.L₁'_exactCategoryTheory.ShortComplex.SnakeInput.L₂'_exact · cited by 3SnakeInput.L₂'_exactCategoryTheory.ShortComplex.SnakeInput.L₀_exact · cited by 3SnakeInput.L₀_exactCategoryTheory.ShortComplex.SnakeInput.composableArrows · cited by 3SnakeInput.composableArro…CategoryTheory.ShortComplex.SnakeInput.L₃_exact · cited by 1SnakeInput.L₃_exactSnakeInput.snake_lemmaCITED BYCITES

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