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Theorems · Inductive type · category theory

CategoryTheory.Precoverage.ZeroHypercover

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.Precoverage C → C → Type (max (max u v) (w + 1))

The type of 0-hypercovers of an object S : C in a category equipped with a coverage J. This can be constructed from a covering of S.

Defined in
Mathlib.CategoryTheory.Sites.Hypercover.Zero
Cited by
81 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
CategoryTheory.Category

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover · cited by 469ZeroHypercover.toPreZeroH…AlgebraicGeometry.Scheme.Cover · cited by 88Scheme.CoverCategoryTheory.Precoverage.ZeroHypercover.pullback₁ · cited by 64ZeroHypercover.pullback₁CategoryTheory.Precoverage.ZeroHypercover.mem₀ · cited by 26ZeroHypercover.mem₀CategoryTheory.Precoverage.mem_iff_exists_zeroHypercover · cited by 8Precoverage.mem_iff_exist…CategoryTheory.Precoverage.ZeroHypercover.Small.restrictFun · cited by 8Small.restrictFunCategoryTheory.Precoverage.ZeroHypercover.bind · cited by 8ZeroHypercover.bindCategoryTheory.Precoverage.ZeroHypercover.restrictIndexOfSmall · cited by 8ZeroHypercover.restrictIn…CategoryTheory.Precoverage.ZeroHypercover.Small · cited by 7ZeroHypercover.SmallCategoryTheory.Precoverage.ZeroHypercover.Small.Index · cited by 4Small.IndexCategoryTheory.MorphismProperty.IsLocalAtTarget.mk_of_iff_of_zeroHypercover · cited by 4IsLocalAtTarget.mk_of_iff…CategoryTheory.Precoverage.ZeroHypercover.pullback₂ · cited by 4ZeroHypercover.pullback₂CategoryTheory.MorphismProperty.iff_of_zeroHypercover_source · cited by 3MorphismProperty.iff_of_z…CategoryTheory.MorphismProperty.iff_of_zeroHypercover_target · cited by 3MorphismProperty.iff_of_z…AlgebraicGeometry.Scheme.precoverage_le_qcPrecoverage_of_isOpenMap · cited by 3Scheme.precoverage_le_qcP…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Precoverage · cited by 204CategoryTheory.PrecoveragePrecoverage.ZeroHypercoverCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by115

Results whose statement or proof uses this declaration.