Theorems · Theorem · category theory
CategoryTheory.cancel_epi
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} (f : X ⟶ Y) [CategoryTheory.Epi f] {g h : Y ⟶ Z},
CategoryTheory.CategoryStruct.comp f g = CategoryTheory.CategoryStruct.comp f h ↔ g = h- Defined in
- Mathlib.CategoryTheory.Category.Basic
- Cited by
- 380 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 11 definitions · uses no axioms
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.Epistatement and proof · cited by 688
- CategoryTheory.Epi.left_cancellationproof · cited by 6
Cited by381
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.IsZero.of_isoproof · cited by 35
- CategoryTheory.ShortComplex.exact_of_g_is_cokernelproof · cited by 25
- CategoryTheory.eq_of_inv_eq_invproof · cited by 19
- AlgebraicGeometry.Scheme.Cover.hom_extproof · cited by 18
- CategoryTheory.IsPullback.of_isoproof · cited by 17
- CategoryTheory.BraidedCategory.braiding_tensor_right_homproof · cited by 14
- CategoryTheory.BraidedCategory.braiding_tensor_left_homproof · cited by 13
- CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitorproof · cited by 12
- CategoryTheory.ShortComplex.Exact.mono_gproof · cited by 10
- CategoryTheory.epi_of_epiproof · cited by 10
- CategoryTheory.IsPushout.of_isoproof · cited by 10
- CategoryTheory.MonoidalCategory.leftUnitor_whiskerRightproof · cited by 9
Showing the 200 most cited of 381.