Theorems · Theorem · category theory
CategoryTheory.Epi.left_cancellation
∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} {X Y : C} {f : X ⟶ Y} [self : CategoryTheory.Epi f] {Z : C}
(g h : Y ⟶ Z), CategoryTheory.CategoryStruct.comp f g = CategoryTheory.CategoryStruct.comp f h → g = hA morphism f is an epimorphism if it can be cancelled when precomposed.
- Defined in
- Mathlib.CategoryTheory.Category.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Epi
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.Epistatement and proof · cited by 688
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.cancel_epiproof · cited by 380
- Profinite.Extend.functor_initialproof · cited by 2
- CommRingCat.epi_iff_epiproof · cited by 2
- AlgebraicGeometry.Spec.basicOpen_hom_extproof · cited by 1
- TopCat.GlueData.rel_equivproof · cited by 1
- CategoryTheory.Adjunction.faithful_R_of_epi_counit_appproof · cited by 0