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Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.Cover.coconeOfLocallyDirected

{P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} →
  {X : AlgebraicGeometry.Scheme} →
    (𝒰 : AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) X) →
      [inst : CategoryTheory.Category.{v_1, u_1} 𝒰.I₀] →
        [inst_1 : 𝒰.LocallyDirected] → CategoryTheory.Limits.Cocone 𝒰.functorOfLocallyDirected

The canonical cocone with point X on the functor induced by the locally directed cover 𝒰. If 𝒰 is an open cover, this is colimiting (see OpenCover.isColimitCoconeOfLocallyDirected).

Defined in
Mathlib.AlgebraicGeometry.Cover.Directed
Cited by
2 results in Mathlib
Foundations
Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryAlgebraicGeometry.Scheme.Cover.LocallyDirected
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AlgebraicGeometry.Scheme.OpenCover.isColimitCoconeOfLocallyDirected · cited by 0OpenCover.isColimitCocone…AlgebraicGeometry.Scheme.Cover.coconeOfLocallyDirected_pt · cited by 0Cover.coconeOfLocallyDire…AlgebraicGeometry.Scheme.Cover.coconeOfLocallyDirected_ι · cited by 0Cover.coconeOfLocallyDire…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…CategoryTheory.PreZeroHypercover.I₀ · cited by 763PreZeroHypercover.I₀CategoryTheory.Limits.Cocone · cited by 746Limits.CoconeCategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover · cited by 469ZeroHypercover.toPreZeroH…AlgebraicGeometry.Scheme.precoverage · cited by 336Scheme.precoverageAlgebraicGeometry.Scheme.Cover · cited by 88Scheme.CoverAlgebraicGeometry.Scheme.Cover.LocallyDirected · cited by 63Cover.LocallyDirectedAlgebraicGeometry.Scheme.Cover.functorOfLocallyDirected · cited by 14Cover.functorOfLocallyDir…AlgebraicGeometry.Scheme.Cover.functorOfLocallyDirectedHomBase · cited by 4Cover.functorOfLocallyDir…Cover.coconeOfLocallyDirectedCITED BYCITES

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