Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Cover.RelativeGluingData.cover_f
∀ {S : AlgebraicGeometry.Scheme} {𝒰 : S.OpenCover} [inst : CategoryTheory.Category.{u_2, u_1} 𝒰.I₀]
[inst_1 : AlgebraicGeometry.Scheme.Cover.LocallyDirected 𝒰] (d : AlgebraicGeometry.Scheme.Cover.RelativeGluingData 𝒰)
[inst_2 : Small.{u, u_1} 𝒰.I₀] [inst_3 : Quiver.IsThin 𝒰.I₀] (j : 𝒰.I₀),
d.cover.f j = CategoryTheory.Limits.colimit.ι d.functor j- Defined in
- Mathlib.AlgebraicGeometry.RelativeGluing
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.PreZeroHypercover.I₀statement and proof · cited by 763
- CategoryTheory.PreZeroHypercover.fstatement and proof · cited by 542
- AlgebraicGeometry.IsOpenImmersionstatement · cited by 476
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverstatement and proof · cited by 469
- CategoryTheory.Limits.colimitstatement · cited by 453
- CategoryTheory.Limits.colimit.ιstatement · cited by 397
- Smallstatement and proof · cited by 369
- AlgebraicGeometry.Scheme.precoveragestatement · cited by 336
Cited by1
Results whose statement or proof uses this declaration.