Theorems · Theorem · algebraic geometry
AlgebraicGeometry.sigmaOpenCover_f
∀ {σ : Type v} (g : σ → AlgebraicGeometry.Scheme) [inst : Small.{u, v} σ] (b : σ),
(AlgebraicGeometry.sigmaOpenCover g).f b = CategoryTheory.Limits.Sigma.ι g b- Defined in
- Mathlib.AlgebraicGeometry.Limits
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Small
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functor.mapstatement · cited by 8,698
- CategoryTheory.Functor.compstatement · cited by 6,529
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.Discretestatement · cited by 2,447
- CategoryTheory.Discrete.functorstatement · cited by 633
- CategoryTheory.PreZeroHypercover.fstatement and proof · cited by 542
- AlgebraicGeometry.IsOpenImmersionstatement · cited by 476
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverstatement and proof · cited by 469
- Smallstatement and proof · cited by 369
- AlgebraicGeometry.Scheme.precoveragestatement · cited by 336
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.exists_hom_isAffine_of_isZariskiLocalAtSourceproof · cited by 1