Theorems · Definition · category theory
CategoryTheory.MonoOver.mk
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{X A : C} → (f : A ⟶ X) → [hf : CategoryTheory.Mono f] → CategoryTheory.MonoOver XConstruct a MonoOver X.
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
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.Monostatement and proof · cited by 893
- CategoryTheory.Over.mkproof · cited by 203
- CategoryTheory.MonoOverstatement · cited by 115
Cited by49
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.mkproof · cited by 109
- CategoryTheory.Subobject.underlyingIsoproof · cited by 41
- CategoryTheory.Subobject.underlyingIso_arrowproof · cited by 22
- CategoryTheory.Abelian.Preradical.colonproof · cited by 13
- CategoryTheory.Subfunctor.equivalenceMonoOverproof · cited by 8
- CategoryTheory.SubobjectRepresentableBy.isostatement and proof · cited by 7
- Types.monoOverEquivalenceSetproof · cited by 6
- CategoryTheory.Subobject.mk_arrowproof · cited by 4
- CategoryTheory.SubobjectRepresentableBy.iso_inv_hom_left_compstatement · cited by 3
- CategoryTheory.SubobjectRepresentableBy.iso_inv_left_πstatement and proof · cited by 3
- CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.Fproof · cited by 3
- CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivity.Fproof · cited by 3