Theorems · Inductive type · category theory
CategoryTheory.MorphismProperty.DescendsAlong
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
CategoryTheory.MorphismProperty C → CategoryTheory.MorphismProperty C → PropP descends along Q if whenever Q holds for X ⟶ Z,
P holds for X ×[Z] Y ⟶ X implies P holds for Y ⟶ Z.
- Cited by
- 16 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.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.MorphismPropertystatement · cited by 2,179
Cited by18
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.of_isPullback_of_descendsAlongstatement and proof · cited by 5
- CategoryTheory.MorphismProperty.DescendsAlong.of_isPullbackstatement and proof · cited by 2
- CategoryTheory.MorphismProperty.iff_of_isPullbackstatement and proof · cited by 2
- AlgebraicGeometry.IsZariskiLocalAtTarget.descendsAlong_inf_quasiCompactstatement · cited by 2
- CategoryTheory.MorphismProperty.DescendsAlong.mk'statement · cited by 1
- CategoryTheory.MorphismProperty.of_pullback_fst_of_descendsAlongstatement and proof · cited by 1
- CategoryTheory.MorphismProperty.of_pullback_snd_of_descendsAlongstatement and proof · cited by 1
- CategoryTheory.MorphismProperty.eq_of_isomorphisms_descendsAlongstatement and proof · cited by 1
- AlgebraicGeometry.IsZariskiLocalAtTarget.descendsAlongstatement · cited by 1
- AlgebraicGeometry.HasRingHomProperty.descendsAlongstatement · cited by 1
- AlgebraicGeometry.HasRingHomProperty.descendsAlong_flatstatement · cited by 0
- CategoryTheory.MorphismProperty.pullback_fst_iffstatement and proof · cited by 0