Theorems · Theorem · category theory
CategoryTheory.ShortComplex.ShortExact.ab_injective_f
∀ {S : CategoryTheory.ShortComplex Ab}, S.ShortExact → Function.Injective ⇑(CategoryTheory.ConcreteCategory.hom S.f)- Defined in
- Mathlib.Algebra.Homology.ShortComplex.Ab
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- AddMonoidHomstatement · cited by 3,230
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.X₂statement · cited by 1,115
- CategoryTheory.ShortComplex.X₁statement · cited by 889
- CategoryTheory.ShortComplex.fstatement and proof · cited by 653
- AddCommGrpCatstatement · cited by 462
- AddCommGrpCat.carrierstatement · cited by 407
- CategoryTheory.ShortComplex.ShortExactstatement and proof · cited by 232
- Abstatement and proof · cited by 198
- CategoryTheory.ShortComplex.ShortExact.mono_fproof · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.ShortExact.ab_finite_iffproof · cited by 0