Theorems · Theorem · category theory
CategoryTheory.mono_of_mono
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} (g : Z ⟶ Y) (f : Y ⟶ X)
[CategoryTheory.Mono (CategoryTheory.CategoryStruct.comp g f)], CategoryTheory.Mono g- Defined in
- Mathlib.CategoryTheory.Category.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.cancel_monoproof · cited by 435
- CategoryTheory.Category.assoc'proof · cited by 19
Cited by9
Results whose statement or proof uses this declaration.
- CategoryTheory.mono_of_mono_facproof · cited by 9
- SimplexCategory.eq_δ_of_monoproof · cited by 4
- CategoryTheory.Functor.PreservesMonomorphisms.of_natTransproof · cited by 2
- CategoryTheory.mono_comp_iff_of_monoproof · cited by 1
- CategoryTheory.Limits.Types.isPushout_of_isPullback_of_monoproof · cited by 1
- SSet.Nonsingular.of_monoproof · cited by 1
- CategoryTheory.ShortComplex.mono_homologyMap_of_mono_opcyclesMap'proof · cited by 0
- CategoryTheory.mem_essImage_of_counit_isSplitEpiproof · cited by 0
- CategoryTheory.strongMono_of_strongMonoproof · cited by 0