Theorems · Definition · category theory
CategoryTheory.MorphismProperty.universally
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.MorphismProperty C → CategoryTheory.MorphismProperty CP.universally holds for a morphism f : X ⟶ Y iff P holds for all X ×[Y] Y' ⟶ Y'.
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- 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.Homproof · cited by 32,603
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.IsPullbackproof · cited by 320
Cited by41
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.UniversallyClosed.universally_isClosedMapstatement · cited by 4
- CategoryTheory.MorphismProperty.universally_eq_iffstatement and proof · cited by 3
- CategoryTheory.MorphismProperty.universally_monostatement and proof · cited by 3
- AlgebraicGeometry.universallyClosed_eqstatement and proof · cited by 2
- AlgebraicGeometry.universallyInjective_eq_diagonalproof · cited by 2
- AlgebraicGeometry.UniversallyClosed.eq_valuativeCriterionproof · cited by 2
- AlgebraicGeometry.UniversallyInjective.universally_injectivestatement · cited by 2
- CategoryTheory.MorphismProperty.universally_lestatement and proof · cited by 2
- AlgebraicGeometry.UniversallyOpen.universally_isOpenMapstatement · cited by 2
- AlgebraicGeometry.geometrically_eq_universallystatement and proof · cited by 2
- AlgebraicGeometry.universallyClosed_eq_universallySpecializingstatement and proof · cited by 1
- AlgebraicGeometry.universallyClosed_iffstatement and proof · cited by 1