Theorems · Theorem · category theory
CategoryTheory.cancel_mono
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} (f : Y ⟶ X) [CategoryTheory.Mono f] {g h : Z ⟶ Y},
CategoryTheory.CategoryStruct.comp g f = CategoryTheory.CategoryStruct.comp h f ↔ g = h- Defined in
- Mathlib.CategoryTheory.Category.Basic
- Cited by
- 435 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.Monostatement and proof · cited by 893
- CategoryTheory.Mono.right_cancellationproof · cited by 4
Cited by436
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.IsZero.of_isoproof · cited by 35
- CategoryTheory.Subobject.eq_of_comp_arrow_eqproof · cited by 31
- CategoryTheory.Functor.ext_of_isoproof · cited by 28
- CategoryTheory.ShortComplex.exact_of_f_is_kernelproof · cited by 22
- CategoryTheory.ShortComplex.exact_iff_exact_up_to_refinementsproof · cited by 14
- CategoryTheory.BraidedCategory.braiding_tensor_right_homproof · cited by 14
- CategoryTheory.BraidedCategory.braiding_tensor_left_homproof · cited by 13
- AlgebraicGeometry.Scheme.isoOfEq_rflproof · cited by 12
- CategoryTheory.ShortComplex.homologyπ_naturalityproof · cited by 10
- CategoryTheory.mono_of_monoproof · cited by 9
- AlgebraicGeometry.morphismRestrict_compproof · cited by 8
- CategoryTheory.ShortComplex.Exact.epi_fproof · cited by 8
Showing the 200 most cited of 436.