Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.of_isPullback_of_descendsAlong

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {P Q : CategoryTheory.MorphismProperty C} {A X Y Z : C}
  {fst : A ⟶ X} {snd : A ⟶ Y} {f : X ⟶ Z} {g : Y ⟶ Z} [P.DescendsAlong Q],
  CategoryTheory.IsPullback fst snd f g → Q f → P fst → P g

Defined in: Mathlib.CategoryTheory.MorphismProperty.Descent
Cited by: 5 results in Mathlib
Foundations: Depth 5 from the axioms · uses no axioms
Assumes: CategoryTheory.Category CategoryTheory.MorphismProperty.DescendsAlong

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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.MorphismPropertystatement and proof · cited by 2,179
CategoryTheory.IsPullbackstatement and proof · cited by 320
CategoryTheory.MorphismProperty.DescendsAlongstatement and proof · cited by 16
CategoryTheory.MorphismProperty.DescendsAlong.of_isPullbackproof · cited by 2

Cited by5

Results whose statement or proof uses this declaration.

CategoryTheory.MorphismProperty.iff_of_isPullbackproof · cited by 2
CategoryTheory.MorphismProperty.of_pullback_fst_of_descendsAlongproof · cited by 1
CategoryTheory.MorphismProperty.of_pullback_snd_of_descendsAlongproof · cited by 1
CategoryTheory.MorphismProperty.eq_of_isomorphisms_descendsAlongproof · cited by 1
AlgebraicGeometry.Scheme.Hom.exists_mem_and_isIso_morphismRestrict_toNormalizationproof · cited by 1