Theorems · Theorem · category theory
CategoryTheory.surjective_up_to_refinements_of_epi
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [CategoryTheory.Abelian C] {X Y : C} (f : X ⟶ Y)
[CategoryTheory.Epi f] {A : C} (y : A ⟶ Y),
∃ A' π,
∃ (_ : CategoryTheory.Epi π), ∃ x, CategoryTheory.CategoryStruct.comp π y = CategoryTheory.CategoryStruct.comp x f- Cited by
- 9 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 · cited by 17,999
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- CategoryTheory.Epistatement and proof · cited by 688
- CategoryTheory.epi_iff_surjective_up_to_refinementsproof · cited by 5
Cited by9
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.SnakeInput.L₁'_exactproof · cited by 4
- CategoryTheory.Abelian.mono_of_epi_of_mono_of_mono'proof · cited by 3
- CategoryTheory.ShortComplex.eq_liftCycles_homologyπ_up_to_refinementsproof · cited by 3
- CategoryTheory.Abelian.epi_of_epi_of_epi_of_mono'proof · cited by 3
- CategoryTheory.Abelian.SpectralObject.Ψ_opcyclesMap_exactproof · cited by 1
- CategoryTheory.IsPushout.hom_eq_add_up_to_refinementsproof · cited by 1
- CategoryTheory.Abelian.SpectralObject.dKernelSequence_exactproof · cited by 1
- CategoryTheory.Abelian.SpectralObject.cokernelSequenceOpcyclesE_exactproof · cited by 1
- CategoryTheory.Abelian.mono_cokernel_map_of_isPullbackproof · cited by 0