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Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.of_pullback_snd_of_descendsAlong

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {P Q : CategoryTheory.MorphismProperty C} {X Y Z : C}
  {f : X ⟶ Z} {g : Y ⟶ Z} [P.DescendsAlong Q] [inst_2 : CategoryTheory.Limits.HasPullback f g],
  Q g → P (CategoryTheory.Limits.pullback.snd f g) → P f
Defined in
Mathlib.CategoryTheory.MorphismProperty.Descent
Cited by
1 results in Mathlib
Foundations
Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.MorphismProperty.DescendsAlongCategoryTheory.Limits.HasPullback
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AlgebraicGeometry.smooth_of_grpObj · cited by 0AlgebraicGeometry.smooth_…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…CategoryTheory.Limits.pullback · cited by 864Limits.pullbackCategoryTheory.Limits.pullback.snd · cited by 637pullback.sndCategoryTheory.Limits.HasPullback · cited by 434Limits.HasPullbackCategoryTheory.IsPullback.of_hasPullback · cited by 70IsPullback.of_hasPullbackCategoryTheory.IsPullback.flip · cited by 61IsPullback.flipCategoryTheory.MorphismProperty.DescendsAlong · cited by 16MorphismProperty.Descends…CategoryTheory.MorphismProperty.of_isPullback_of_descendsAlong · cited by 5MorphismProperty.of_isPul…MorphismProperty.of_pullback_…CITED BYCITES

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