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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
Defined in
Mathlib.AlgebraicGeometry.Morphisms.Basic
Cited by
8 results in Mathlib
Foundations
Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.MorphismProperty.RespectsIsoCategoryTheory.IsIsoAlgebraicGeometry.IsAffine

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.HasAffineProperty.iff_of_isAffine · cited by 21HasAffineProperty.iff_of_…AlgebraicGeometry.HasAffineProperty.isStableUnderBaseChange · cited by 3HasAffineProperty.isStabl…AlgebraicGeometry.HasAffineProperty.diagonal_of_openCover · cited by 2HasAffineProperty.diagona…AlgebraicGeometry.AffineTargetMorphismProperty.IsStableUnderBaseChange.mk · cited by 2IsStableUnderBaseChange.mkAlgebraicGeometry.of_targetAffineLocally_of_isPullback · cited by 2AlgebraicGeometry.of_targ…AlgebraicGeometry.HasAffineProperty.diagonal_of_diagonal_of_isPullback · cited by 1HasAffineProperty.diagona…AlgebraicGeometry.AffineTargetMorphismProperty.diagonal_of_openCover_source · cited by 1AffineTargetMorphismPrope…AlgebraicGeometry.HasAffineProperty.diagonal_iff · cited by 1HasAffineProperty.diagona…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.IsIso · cited by 1156CategoryTheory.IsIsoCategoryTheory.MorphismProperty.RespectsIso · cited by 248MorphismProperty.Respects…AlgebraicGeometry.IsAffine · cited by 159AlgebraicGeometry.IsAffineCategoryTheory.MorphismProperty.cancel_left_of_respectsIso · cited by 33MorphismProperty.cancel_l…AlgebraicGeometry.AffineTargetMorphismProperty · cited by 31AlgebraicGeometry.AffineT…AlgebraicGeometry.AffineTargetMorphismProperty.toProperty · cited by 9AffineTargetMorphismPrope…AlgebraicGeometry.AffineTargetMorphismProperty.toProperty_apply · cited by 3AffineTargetMorphismPrope…AffineTargetMorphismProperty.…CITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by8

Results whose statement or proof uses this declaration.