Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst

∀ {T : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} T] {P Q : CategoryTheory.MorphismProperty T}
  [inst_1 : Q.IsMultiplicative] {X Y : T} {f : X ⟶ Y} [inst_2 : P.HasPullbacksAlong f] {g : X ⟶ Y}
  [inst_3 : P.IsStableUnderBaseChangeAlong f] [inst_4 : Q.IsStableUnderBaseChange] (h : f = g) (A : P.Over Q Y),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.MorphismProperty.Over.pullbackCongr h).hom.app A).left
      (CategoryTheory.Limits.pullback.fst A.hom g) =
    CategoryTheory.Limits.pullback.fst A.hom f

Defined in

Mathlib.CategoryTheory.MorphismProperty.OverAdjunction

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.HasPullbacksAlongCategoryTheory.MorphismProperty.IsStableUnderBaseChangeAlongCategoryTheory.MorphismProperty.IsStableUnderBaseChange