Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Cover.pushforwardIso
{P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} →
[P.RespectsIso] →
[P.ContainsIdentities] →
[P.IsStableUnderComposition] →
{X Y : AlgebraicGeometry.Scheme} →
AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) X →
(f : X ⟶ Y) →
[CategoryTheory.IsIso f] → AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) YThe pushforward of a cover along an isomorphism.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- Equiv.symmproof · cited by 3,681
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.PreZeroHypercover.I₀proof · cited by 763
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.PreZeroHypercover.Xproof · cited by 649
- CategoryTheory.PreZeroHypercover.fproof · cited by 542
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverproof · cited by 469
- Equiv.transproof · cited by 337
Cited by5
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Pullback.openCoverOfRightproof · cited by 4
- AlgebraicGeometry.HasAffineProperty.diagonal_iffproof · cited by 1
- AlgebraicGeometry.Scheme.Cover.pushforwardIso_I₀statement and proof · cited by 0
- AlgebraicGeometry.Scheme.Cover.pushforwardIso_Xstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.Cover.pushforwardIso_fstatement and proof · cited by 0