Theorems · Theorem · category theory
CategoryTheory.mono_comp_iff_of_isIso
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y Z : C} (g : Z ⟶ Y) [CategoryTheory.IsIso g]
(f : Y ⟶ X), CategoryTheory.Mono (CategoryTheory.CategoryStruct.comp g f) ↔ CategoryTheory.Mono fWhen f is an isomorphism, f ≫ g is monic iff g is.
- Defined in
- Mathlib.CategoryTheory.EpiMono
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.Category.id_compproof · cited by 1,998
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.invproof · cited by 467
- CategoryTheory.IsIso.inv_hom_idproof · cited by 88
- CategoryTheory.Category.assoc'proof · cited by 19
Cited by3
Results whose statement or proof uses this declaration.