Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionCocone

{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 j : 𝒰.I₀} →
                        (hij : i ⟶ j) →
                          CategoryTheory.Limits.Cocone
                            (D.comp
                              ((CategoryTheory.MorphismProperty.Over.pullback P ⊤ (𝒰.f i)).comp
                                (CategoryTheory.MorphismProperty.Over.map ⊤ ⋯)))

(Implementation) Cocone for transition map for construction of AlgebraicGeometry.Scheme.Cover.ColimitGluingData.functor.

Defined in

Mathlib.AlgebraicGeometry.ColimitsOver

Cited by

2 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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