Theorems · Definition · category theory
CategoryTheory.MorphismProperty.Over.mk
{T : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} T] →
{P : CategoryTheory.MorphismProperty T} →
(Q : CategoryTheory.MorphismProperty T) → {X A : T} → (f : A ⟶ X) → P f → P.Over Q XMake an object of P.Over Q X from a morphism f : A ⟶ X and a proof of P f.
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.MorphismProperty.Overstatement · cited by 94
Cited by20
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.Over.pullbackproof · cited by 42
- AlgebraicGeometry.Scheme.Cover.ColimitGluingData.gluedproof · cited by 7
- CategoryTheory.MorphismProperty.overEquivOfIsInitialproof · cited by 4
- AlgebraicGeometry.Scheme.ProEt.mkproof · cited by 3
- CategoryTheory.MorphismProperty.CostructuredArrow.toOverproof · cited by 2
- AlgebraicGeometry.Scheme.Etale.mkproof · cited by 2
- AlgebraicGeometry.IsClosedImmersion.isIso_of_ker_eqproof · cited by 2
- CategoryTheory.MorphismProperty.exists_map_eq_of_presieveproof · cited by 2
- AlgebraicGeometry.IsClosedImmersion.overEquivIdealSheafDataproof · cited by 1
- CategoryTheory.MorphismProperty.CostructuredArrow.toOver_mapstatement · cited by 0
- AlgebraicGeometry.Scheme.AffineEtale.Spec_map_leftstatement · cited by 0
- CategoryTheory.MorphismProperty.CostructuredArrow.toOver_objstatement · cited by 0