Theorems · Theorem · category theory
CategoryTheory.ShortComplex.ShortExact.epi_g
∀ {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.Epi S.g- Cited by
- 17 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.ShortComplex.X₃statement · cited by 876
- CategoryTheory.Epistatement · cited by 688
- CategoryTheory.ShortComplex.gstatement · cited by 658
- CategoryTheory.ShortComplex.ShortExactstatement and proof · cited by 232
Cited by17
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.ShortExact.map_of_exactproof · cited by 23
- CategoryTheory.ShortComplex.ShortExact.homology_exact₂proof · cited by 6
- CategoryTheory.Functor.exact_tfaeproof · cited by 3
- HomologicalComplex.HomologySequence.epi_homologyMap_τ₃proof · cited by 1
- CategoryTheory.ObjectProperty.prop_X₃_of_shortExactproof · cited by 1
- CategoryTheory.ShortComplex.ShortExact.ab_surjective_gproof · cited by 1
- HomologicalComplex.HomologySequence.mono_homologyMap_τ₃proof · cited by 1
- CategoryTheory.ShortComplex.ShortExact.surjective_gproof · cited by 1
- TopCat.Sheaf.IsFlasque.epi_of_shortExactproof · cited by 1
- CategoryTheory.ShortComplex.ShortExact.exactAt_X₃proof · cited by 1
- CategoryTheory.ShortComplex.isIso₂_of_shortExact_of_isIso₁₃proof · cited by 1
- CategoryTheory.JointlyReflectIsomorphisms.shortExact_iffproof · cited by 0