Theorems · Theorem · category theory
CategoryTheory.Mono.right_cancellation
∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} {X Y : C} {f : X ⟶ Y} [self : CategoryTheory.Mono f] {Z : C}
(g h : Z ⟶ X), CategoryTheory.CategoryStruct.comp g f = CategoryTheory.CategoryStruct.comp h f → g = hA morphism f is a monomorphism if it can be cancelled when postcomposed.
- Defined in
- Mathlib.CategoryTheory.Category.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Mono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.Monostatement and proof · cited by 893
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.cancel_monoproof · cited by 435
- CategoryTheory.GlueData.t'_iijproof · cited by 1
- CategoryTheory.Adjunction.faithful_L_of_mono_unit_appproof · cited by 0
- CategoryTheory.Presieve.firstMap_eq_secondMapproof · cited by 0