Theorems · Theorem · category theory
CategoryTheory.mono_of_mono_fac
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} {f : Y ⟶ X} {g : Z ⟶ Y} {h : Z ⟶ X}
[CategoryTheory.Mono h], CategoryTheory.CategoryStruct.comp g f = h → CategoryTheory.Mono g- Defined in
- Mathlib.CategoryTheory.Category.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 and proof · cited by 17,999
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.mono_of_monoproof · cited by 9
Cited by9
Results whose statement or proof uses this declaration.
- SSet.Subcomplex.isIso_toOfSimplex_iffproof · cited by 1
- CategoryTheory.Abelian.mono_inl_of_isColimitproof · cited by 1
- CategoryTheory.Limits.InitialMonoClass.of_isTerminalproof · cited by 1
- CategoryTheory.ShortComplex.Exact.isIso_f'proof · cited by 1
- AlgebraicGeometry.IsOpenImmersion.of_flat_of_monoproof · cited by 0
- CategoryTheory.Abelian.mono_inr_of_isColimitproof · cited by 0
- CategoryTheory.Abelian.SpectralObject.mono_mapproof · cited by 0
- CategoryTheory.ComposableArrows.IsComplex.mono_cokerToKer'proof · cited by 0