Theorems · Definition · category theory
CategoryTheory.Abelian.factorThruCoimage
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
{P Q : C} →
(f : P ⟶ Q) →
[inst_2 : CategoryTheory.Limits.HasKernel f] →
[inst_3 : CategoryTheory.Limits.HasCokernel (CategoryTheory.Limits.kernel.ι f)] →
CategoryTheory.Abelian.coimage f ⟶ QThere is a canonical monomorphism i : coimage f ⟶ Q.
- Defined in
- Mathlib.CategoryTheory.Abelian.Images
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.Limits.kernelstatement · cited by 272
- CategoryTheory.Limits.kernel.ιstatement and proof · cited by 214
- CategoryTheory.Limits.HasKernelstatement and proof · cited by 169
- CategoryTheory.Limits.HasCokernelstatement and proof · cited by 131
- CategoryTheory.Limits.cokernel.descproof · cited by 53
- CategoryTheory.Limits.kernel.conditionproof · cited by 52
- CategoryTheory.Abelian.coimagestatement · cited by 44
Cited by15
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.coimageStrongEpiMonoFactorisationproof · cited by 5
- CategoryTheory.Functor.preservesFiniteLimits_tfaeproof · cited by 5
- CategoryTheory.ShortComplex.RightHomologyData.ofAbelianproof · cited by 4
- CategoryTheory.Abelian.comp_coimage_π_eq_zeroproof · cited by 3
- CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_invstatement and proof · cited by 2
- CategoryTheory.ObjectProperty.exists_comp_monoModSerre_eq_zero_iffproof · cited by 2
- CategoryTheory.ShortComplex.exact_iff_exact_coimage_πproof · cited by 2
- CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_homstatement and proof · cited by 1
- CategoryTheory.Abelian.coimageStrongEpiMonoFactorisation_mstatement · cited by 1
- CategoryTheory.Functor.preservesHomology_of_preservesMonos_and_cokernelsproof · cited by 1
- CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_hom_assocstatement and proof · cited by 0
- CategoryTheory.Abelian.PreservesCoimage.factorThruCoimage_iso_inv_assocstatement and proof · cited by 0