Theorems · Definition · category theory

CategoryTheory.ShortComplex.Splitting.unop

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] → {S : CategoryTheory.ShortComplex Cᵒᵖ} → S.Splitting → S.unop.Splitting

The splitting of the short complex S.unop deduced from a splitting of S.

Defined in: Mathlib.Algebra.Homology.ShortComplex.Exact
Cited by: 2 results in Mathlib
Foundations: Depth 27 from the axioms · uses propext, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive

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Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Oppositestatement and proof · cited by 8,081
CategoryTheory.Preadditivestatement and proof · cited by 3,309
CategoryTheory.ShortComplexstatement and proof · cited by 1,850
Quiver.Hom.unopproof · cited by 903
CategoryTheory.ShortComplex.Splittingstatement and proof · cited by 62
CategoryTheory.ShortComplex.unopstatement · cited by 44
CategoryTheory.ShortComplex.Splitting.sproof · cited by 24
CategoryTheory.ShortComplex.Splitting.rproof · cited by 24

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.ShortComplex.Splitting.unop_rstatement and proof · cited by 0
CategoryTheory.ShortComplex.Splitting.unop_sstatement and proof · cited by 0