Theorems · Theorem · category theory

CategoryTheory.ShortComplex.ShortExact.isIso_g_iff

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  {S : CategoryTheory.ShortComplex C},
  S.ShortExact → ∀ [CategoryTheory.Balanced C], CategoryTheory.IsIso S.g ↔ CategoryTheory.Limits.IsZero S.X₁

Defined in: Mathlib.Algebra.Homology.ShortComplex.ShortExact
Cited by: 0 results in Mathlib
Foundations: Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive CategoryTheory.Balanced

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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
Quiver.Homproof · cited by 32,603
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.CategoryStruct.idproof · cited by 6,235
CategoryTheory.Preadditivestatement and proof · cited by 3,309
CategoryTheory.ShortComplexstatement and proof · cited by 1,850
CategoryTheory.Limits.HasZeroObjectproof · cited by 1,298
CategoryTheory.IsIsostatement and proof · cited by 1,156
CategoryTheory.ShortComplex.X₂statement and proof · cited by 1,115
CategoryTheory.Monoproof · cited by 893
CategoryTheory.ShortComplex.X₁statement and proof · cited by 889

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