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Theorems · Definition · category theory

CategoryTheory.ShortComplex.SnakeInput.functorP

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

The functor which sends S : SnakeInput C to the auxiliary object S.P, which is pullback S.L₁.g S.v₀₁.τ₃.

Defined in
Mathlib.Algebra.Homology.ShortComplex.SnakeLemma
Cited by
7 results in Mathlib
Foundations
Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Abelian
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Around this declaration

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

CategoryTheory.ShortComplex.SnakeInput.naturality_δ · cited by 3SnakeInput.naturality_δCategoryTheory.ShortComplex.SnakeInput.naturality_φ₂ · cited by 1SnakeInput.naturality_φ₂CategoryTheory.ShortComplex.SnakeInput.functorP_map · cited by 1SnakeInput.functorP_mapCategoryTheory.ShortComplex.SnakeInput.naturality_φ₁ · cited by 1SnakeInput.naturality_φ₁CategoryTheory.ShortComplex.SnakeInput.naturality_φ₁_assoc · cited by 1SnakeInput.naturality_φ₁_…CategoryTheory.ShortComplex.SnakeInput.functorP_obj · cited by 0SnakeInput.functorP_objCategoryTheory.ShortComplex.SnakeInput.naturality_φ₂_assoc · cited by 0SnakeInput.naturality_φ₂_…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianCategoryTheory.ShortComplex.g · cited by 658ShortComplex.gCategoryTheory.ShortComplex.Hom.τ₂ · cited by 243Hom.τ₂CategoryTheory.ShortComplex.Hom.τ₃ · cited by 197Hom.τ₃CategoryTheory.Limits.pullback.map · cited by 156pullback.mapCategoryTheory.ShortComplex.SnakeInput · cited by 129ShortComplex.SnakeInputCategoryTheory.ShortComplex.SnakeInput.L₁ · cited by 70SnakeInput.L₁CategoryTheory.ShortComplex.SnakeInput.v₀₁ · cited by 43SnakeInput.v₀₁CategoryTheory.ShortComplex.SnakeInput.Hom.f₀ · cited by 19Hom.f₀CategoryTheory.ShortComplex.SnakeInput.Hom.f₁ · cited by 16Hom.f₁CategoryTheory.ShortComplex.SnakeInput.P · cited by 15SnakeInput.PSnakeInput.functorPCITED BYCITES

Cites14

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Cited by7

Results whose statement or proof uses this declaration.