Theorems · Theorem · category theory
CategoryTheory.ShortComplex.shortExact_of_iso
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S₁ S₂ : CategoryTheory.ShortComplex C} (e : S₁ ≅ S₂), S₁.ShortExact → S₂.ShortExact- Cited by
- 2 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- CategoryTheory.Isostatement and proof · cited by 3,963
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.ShortExactstatement and proof · cited by 232
- CategoryTheory.ShortComplex.ShortExact.exactproof · cited by 20
- CategoryTheory.ShortComplex.exact_of_isoproof · cited by 18
Cited by2
Results whose statement or proof uses this declaration.
- TateCohomology.map_tateComplexFunctor_shortExactproof · cited by 5
- CategoryTheory.ShortComplex.shortExact_iff_of_isoproof · cited by 0