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Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.Cover.gluedCover

{X : AlgebraicGeometry.Scheme} → X.OpenCover → AlgebraicGeometry.Scheme.GlueData

The glue data associated with an open cover. The canonical isomorphism 𝒰.gluedCover.glued ⟶ X is provided by 𝒰.fromGlued.

Defined in
Mathlib.AlgebraicGeometry.Gluing
Cited by
15 results in Mathlib
Foundations
Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

AlgebraicGeometry.Scheme.Cover.hom_ext · cited by 18Cover.hom_extAlgebraicGeometry.Scheme.Cover.ι_glueMorphisms · cited by 12Cover.ι_glueMorphismsAlgebraicGeometry.Scheme.Cover.glueMorphisms · cited by 10Cover.glueMorphismsAlgebraicGeometry.Scheme.Cover.fromGlued · cited by 9Cover.fromGluedAlgebraicGeometry.Scheme.Cover.ι_fromGlued · cited by 2Cover.ι_fromGluedAlgebraicGeometry.Scheme.Cover.fromGlued_injective · cited by 2Cover.fromGlued_injectiveAlgebraicGeometry.Scheme.Cover.isOpenMap_fromGlued · cited by 1Cover.isOpenMap_fromGluedAlgebraicGeometry.Scheme.Cover.gluedCover_J · cited by 0Cover.gluedCover_JAlgebraicGeometry.Scheme.Cover.gluedCover_U · cited by 0Cover.gluedCover_UAlgebraicGeometry.Scheme.Cover.gluedCover_V · cited by 0Cover.gluedCover_VAlgebraicGeometry.Scheme.Cover.gluedCover_f · cited by 0Cover.gluedCover_fAlgebraicGeometry.Scheme.Cover.gluedCover_t · cited by 0Cover.gluedCover_tAlgebraicGeometry.Scheme.Cover.gluedCover_t' · cited by 0Cover.gluedCover_t'AlgebraicGeometry.Scheme.Pullback.gluedLift_p1 · cited by 0Pullback.gluedLift_p1AlgebraicGeometry.Scheme.Pullback.gluedLift_p2 · cited by 0Pullback.gluedLift_p2CategoryTheory.Iso.hom · cited by 7684Iso.homAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.Limits.pullback · cited by 864Limits.pullbackCategoryTheory.PreZeroHypercover.I₀ · cited by 763PreZeroHypercover.I₀CategoryTheory.PreZeroHypercover.X · cited by 649PreZeroHypercover.XCategoryTheory.Limits.pullback.fst · cited by 639pullback.fstCategoryTheory.PreZeroHypercover.f · cited by 542PreZeroHypercover.fCategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercover · cited by 469ZeroHypercover.toPreZeroH…AlgebraicGeometry.Scheme.OpenCover · cited by 207Scheme.OpenCoverCategoryTheory.Limits.pullbackSymmetry · cited by 61Limits.pullbackSymmetryAlgebraicGeometry.Scheme.GlueData · cited by 23Scheme.GlueDataAlgebraicGeometry.Scheme.Cover.gluedCoverT' · cited by 12Cover.gluedCoverT'AlgebraicGeometry.Scheme.Cover.glued_cover_cocycle · cited by 0Cover.glued_cover_cocycleCover.gluedCoverCITED BYCITES

Cites13

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

Cited by17

Results whose statement or proof uses this declaration.