Theorems · Theorem · algebraic geometry
AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict_assoc
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : AlgebraicGeometry.SheafedSpace C} (f : X ⟶ Y)
[H : AlgebraicGeometry.SheafedSpace.IsOpenImmersion f] {Z : AlgebraicGeometry.SheafedSpace C} (h : Y ⟶ Z),
CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.SheafedSpace.IsOpenImmersion.isoRestrict f).hom
(CategoryTheory.CategoryStruct.comp (Y.ofRestrict ⋯) h) =
CategoryTheory.CategoryStruct.comp f h- Cited by
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- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Iso.homstatement and proof · cited by 7,684
- CategoryTheory.Category.assocproof · cited by 6,433
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.PresheafedSpace.Hom.basestatement · cited by 1,135
- CategoryTheory.InducedCategory.Hom.homstatement · cited by 850
- AlgebraicGeometry.PresheafedSpacestatement · cited by 260
- AlgebraicGeometry.SheafedSpacestatement and proof · cited by 142
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.base_openstatement and proof · cited by 24
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