Theorems · Theorem · algebraic geometry
AlgebraicGeometry.AffineTargetMorphismProperty.cancel_left_of_respectsIso
∀ (P : AlgebraicGeometry.AffineTargetMorphismProperty) [P.toProperty.RespectsIso] {X Y Z : AlgebraicGeometry.Scheme}
(f : X ⟶ Y) (g : Y ⟶ Z) [CategoryTheory.IsIso f] [inst : AlgebraicGeometry.IsAffine Z],
P (CategoryTheory.CategoryStruct.comp f g) ↔ P g- Cited by
- 8 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.MorphismProperty.RespectsIsostatement and proof · cited by 248
- AlgebraicGeometry.IsAffinestatement and proof · cited by 159
- CategoryTheory.MorphismProperty.cancel_left_of_respectsIsoproof · cited by 33
- AlgebraicGeometry.AffineTargetMorphismPropertystatement and proof · cited by 31
- AlgebraicGeometry.AffineTargetMorphismProperty.toPropertystatement and proof · cited by 9
- AlgebraicGeometry.AffineTargetMorphismProperty.toProperty_applyproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.HasAffineProperty.iff_of_isAffineproof · cited by 21
- AlgebraicGeometry.HasAffineProperty.isStableUnderBaseChangeproof · cited by 3
- AlgebraicGeometry.HasAffineProperty.diagonal_of_openCoverproof · cited by 2
- AlgebraicGeometry.of_targetAffineLocally_of_isPullbackproof · cited by 2
- AlgebraicGeometry.HasAffineProperty.diagonal_of_diagonal_of_isPullbackproof · cited by 1
- AlgebraicGeometry.HasAffineProperty.diagonal_iffproof · cited by 1