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Theorems · Definition · category theory

CategoryTheory.ShortComplex.SnakeInput.op

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Abelian C] →
      CategoryTheory.ShortComplex.SnakeInput C → CategoryTheory.ShortComplex.SnakeInput Cᵒᵖ

The snake input in the opposite category that is deduced from a snake input.

Defined in
Mathlib.Algebra.Homology.ShortComplex.SnakeLemma
Cited by
10 results in Mathlib
Foundations
Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Abelian

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.ShortComplex.SnakeInput.L₂'_exact · cited by 3SnakeInput.L₂'_exactCategoryTheory.ShortComplex.SnakeInput.L₂'OpIso · cited by 1SnakeInput.L₂'OpIsoCategoryTheory.ShortComplex.SnakeInput.L₃_exact · cited by 1SnakeInput.L₃_exactCategoryTheory.ShortComplex.SnakeInput.P'IsoUnopOpP · cited by 1SnakeInput.P'IsoUnopOpPCategoryTheory.ShortComplex.SnakeInput.PIsoUnopOpP' · cited by 1SnakeInput.PIsoUnopOpP'CategoryTheory.ShortComplex.SnakeInput.op_L₀ · cited by 0SnakeInput.op_L₀CategoryTheory.ShortComplex.SnakeInput.op_L₁ · cited by 0SnakeInput.op_L₁CategoryTheory.ShortComplex.SnakeInput.op_L₂ · cited by 0SnakeInput.op_L₂CategoryTheory.ShortComplex.SnakeInput.op_L₃ · cited by 0SnakeInput.op_L₃CategoryTheory.ShortComplex.SnakeInput.op_v₀₁ · cited by 0SnakeInput.op_v₀₁CategoryTheory.ShortComplex.SnakeInput.op_v₁₂ · cited by 0SnakeInput.op_v₁₂CategoryTheory.ShortComplex.SnakeInput.op_v₂₃ · cited by 0SnakeInput.op_v₂₃CategoryTheory.ShortComplex.SnakeInput.op_δ · cited by 0SnakeInput.op_δCategoryTheory.Category · cited by 32673CategoryTheory.CategoryOpposite · cited by 8081OppositeCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianCategoryTheory.Equivalence.functor · cited by 1268Equivalence.functorCategoryTheory.ShortComplex.SnakeInput · cited by 129ShortComplex.SnakeInputCategoryTheory.ShortComplex.op · cited by 88ShortComplex.opCategoryTheory.ShortComplex.SnakeInput.L₂ · cited by 71SnakeInput.L₂CategoryTheory.ShortComplex.SnakeInput.L₁ · cited by 70SnakeInput.L₁CategoryTheory.ShortComplex.SnakeInput.L₀ · cited by 69SnakeInput.L₀CategoryTheory.ShortComplex.SnakeInput.L₃ · cited by 60SnakeInput.L₃CategoryTheory.ShortComplex.SnakeInput.v₁₂ · cited by 47SnakeInput.v₁₂CategoryTheory.ShortComplex.SnakeInput.v₀₁ · cited by 43SnakeInput.v₀₁CategoryTheory.ShortComplex.opMap · cited by 42ShortComplex.opMapCategoryTheory.ShortComplex.SnakeInput.v₂₃ · cited by 34SnakeInput.v₂₃CategoryTheory.ShortComplex.opEquiv · cited by 4ShortComplex.opEquivSnakeInput.opCITED BYCITES

Cites23

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Cited by13

Results whose statement or proof uses this declaration.