Theorems · Theorem · category theory
CategoryTheory.ShortComplex.ShortExact.mono_f
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S : CategoryTheory.ShortComplex C}, S.ShortExact → CategoryTheory.Mono S.f- Cited by
- 19 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.X₂statement · cited by 1,115
- CategoryTheory.Monostatement · cited by 893
- CategoryTheory.ShortComplex.X₁statement · cited by 889
- CategoryTheory.ShortComplex.fstatement · cited by 653
- CategoryTheory.ShortComplex.ShortExactstatement and proof · cited by 232
Cited by19
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.ShortExact.map_of_exactproof · cited by 23
- groupHomology.map_chainsFunctor_shortExactproof · cited by 8
- CategoryTheory.Functor.exact_tfaeproof · cited by 3
- CategoryTheory.ObjectProperty.prop_X₁_of_shortExactproof · cited by 1
- CategoryTheory.ShortComplex.ShortExact.ab_injective_fproof · cited by 1
- CategoryTheory.ShortComplex.ShortExact.d_eq_zero_of_f_eq_d_applyproof · cited by 1
- TopCat.Sheaf.IsFlasque.epi_of_shortExactproof · cited by 1
- CategoryTheory.ShortComplex.ShortExact.exactAt_X₁proof · cited by 1
- CategoryTheory.ShortComplex.isIso₂_of_shortExact_of_isIso₁₃proof · cited by 1
- groupHomology.mem_cycles₁_of_comp_eq_d₂₁proof · cited by 1
- groupCohomology.mem_cocycles₁_of_comp_eq_d₀₁proof · cited by 1
- groupCohomology.mem_cocycles₂_of_comp_eq_d₁₂proof · cited by 1