Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.homOfLE_homOfLE_assoc
∀ (X : AlgebraicGeometry.Scheme) {U V W : X.Opens} (e₁ : U ≤ V) (e₂ : V ≤ W) {Z : AlgebraicGeometry.Scheme}
(h : ↑W ⟶ Z),
CategoryTheory.CategoryStruct.comp (X.homOfLE e₁) (CategoryTheory.CategoryStruct.comp (X.homOfLE e₂) h) =
CategoryTheory.CategoryStruct.comp (X.homOfLE ⋯) h- Defined in
- Mathlib.AlgebraicGeometry.Restrict
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- CategoryTheory.Category.assocproof · cited by 6,433
- TopCat.carrierstatement · cited by 3,184
- LE.le.transstatement and proof · cited by 3,151
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
- AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.PartialMap.equiv_iff_of_isSeparated_of_leproof · cited by 2
- AlgebraicGeometry.Scheme.PartialMap.equiv.transproof · cited by 2
- AlgebraicGeometry.morphismRestrict_ι_image_ι_isoImage_invproof · cited by 1
- AlgebraicGeometry.Scheme.PartialMap.comp_restrict_leftproof · cited by 1
- AlgebraicGeometry.Scheme.PartialMap.restrict_restrictproof · cited by 0
- AlgebraicGeometry.Scheme.PartialMap.restrict_restrict_homproof · cited by 0