Theorems · Theorem · category theory
CategoryTheory.ShortComplex.Exact.descToInjective.congr_simp
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Abelian C]
{S : CategoryTheory.ShortComplex C} (hS : S.Exact) {J : C} (f f_1 : S.X₂ ⟶ J) (e_f : f = f_1)
[inst_2 : CategoryTheory.Injective J] (hf : CategoryTheory.CategoryStruct.comp S.f f = 0),
hS.descToInjective f hf = hS.descToInjective f_1 ⋯- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- CategoryTheory.ShortComplex.X₂statement and proof · cited by 1,115
- CategoryTheory.ShortComplex.X₁statement · cited by 889
- CategoryTheory.ShortComplex.X₃statement · cited by 876
- CategoryTheory.ShortComplex.fstatement and proof · cited by 653
- CategoryTheory.ShortComplex.Exactstatement and proof · cited by 292
- CategoryTheory.Injectivestatement and proof · cited by 70
- CategoryTheory.ShortComplex.Exact.descToInjectivestatement and proof · cited by 4
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