Theorems · Theorem · algebraic geometry

CategoryTheory.MorphismProperty.Over.mapPullbackAdj.congr_simp

∀ {T : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} T] (P Q : CategoryTheory.MorphismProperty T)
  [inst_1 : Q.IsMultiplicative] {X Y : T} [inst_2 : P.IsStableUnderComposition] [inst_3 : Q.IsStableUnderBaseChange]
  (f : X ⟶ Y) [inst_4 : P.HasPullbacksAlong f] [inst_5 : P.IsStableUnderBaseChangeAlong f]
  [inst_6 : Q.HasOfPostcompProperty Q] (hPf : P f) (hQf : Q f),
  CategoryTheory.MorphismProperty.Over.mapPullbackAdj P Q f hPf hQf =
    CategoryTheory.MorphismProperty.Over.mapPullbackAdj P Q f hPf hQf

Defined in

Mathlib.AlgebraicGeometry.ColimitsOver

Cited by

0 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.IsStableUnderCompositionCategoryTheory.MorphismProperty.IsStableUnderBaseChangeCategoryTheory.MorphismProperty.HasPullbacksAlongCategoryTheory.MorphismProperty.IsStableUnderBaseChangeAlongCategoryTheory.MorphismProperty.HasOfPostcompProperty