Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Cover.ColimitGluingData.prop_trans

∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} [inst : P.IsStableUnderBaseChange]
  {S : AlgebraicGeometry.Scheme} {J : Type u_1} [inst_1 : CategoryTheory.Category.{v_1, u_1} J]
  {D : CategoryTheory.Functor J (P.Over ⊤ S)} {𝒰 : S.OpenCover} [inst_2 : CategoryTheory.Category.{v_3, u_2} 𝒰.I₀]
  [inst_3 : AlgebraicGeometry.Scheme.Cover.LocallyDirected 𝒰]
  (self : AlgebraicGeometry.Scheme.Cover.ColimitGluingData D 𝒰) {i j : 𝒰.I₀} (hij : i ⟶ j),
  P (AlgebraicGeometry.Scheme.Cover.trans 𝒰 hij)

Defined in

Mathlib.AlgebraicGeometry.ColimitsOver

Cited by

9 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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