Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.OpenCover.isColimitCoconeOfLocallyDirected
{X : AlgebraicGeometry.Scheme} →
(𝒰 : X.OpenCover) →
[inst : CategoryTheory.Category.{v_1, u_1} 𝒰.I₀] →
[inst_1 : AlgebraicGeometry.Scheme.Cover.LocallyDirected 𝒰] →
CategoryTheory.Limits.IsColimit (AlgebraicGeometry.Scheme.Cover.coconeOfLocallyDirected 𝒰)If 𝒰 is an open cover of X that is locally directed, X is
the colimit of the components of 𝒰.
- Defined in
- Mathlib.AlgebraicGeometry.Cover.Directed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.NatTrans.appproof · cited by 7,406
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.Limits.IsColimitstatement · cited by 773
- CategoryTheory.PreZeroHypercover.I₀statement and proof · cited by 763
- CategoryTheory.Limits.Coconeproof · cited by 746
- CategoryTheory.Limits.Cocone.ιproof · cited by 605
- AlgebraicGeometry.IsOpenImmersionstatement · cited by 476
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverstatement and proof · cited by 469
- AlgebraicGeometry.Scheme.precoveragestatement · cited by 336
- AlgebraicGeometry.Scheme.OpenCoverstatement and proof · cited by 207
- AlgebraicGeometry.Scheme.Cover.LocallyDirectedstatement and proof · cited by 63
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