Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_id

∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} [inst : P.IsStableUnderBaseChange]
  [inst_1 : P.IsMultiplicative] {S : AlgebraicGeometry.Scheme} {J : Type u_1}
  [inst_2 : CategoryTheory.Category.{v_1, u_1} J] {D : CategoryTheory.Functor J (P.Over ⊤ S)} {𝒰 : S.OpenCover}
  [inst_3 : CategoryTheory.Category.{v_2, u_2} 𝒰.I₀] [inst_4 : AlgebraicGeometry.Scheme.Cover.LocallyDirected 𝒰]
  (d : AlgebraicGeometry.Scheme.Cover.ColimitGluingData D 𝒰) (i : 𝒰.I₀),
  d.transitionMap (CategoryTheory.CategoryStruct.id i) =
    (CategoryTheory.MorphismProperty.Over.mapId ⊤ (𝒰.X i)
            (AlgebraicGeometry.Scheme.Cover.trans 𝒰 (CategoryTheory.CategoryStruct.id i)) ⋯).hom.app
      (d.cocone i).pt

Defined in

Mathlib.AlgebraicGeometry.ColimitsOver

Cited by

0 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.MorphismProperty.IsStableUnderBaseChangeCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.CategoryCategoryTheory.CategoryAlgebraicGeometry.Scheme.Cover.LocallyDirected