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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullback_cone_of_left_condition

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : AlgebraicGeometry.PresheafedSpace C} (f : X ⟶ Z)
  [hf : AlgebraicGeometry.PresheafedSpace.IsOpenImmersion f] (g : Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeftFst f g) f =
    CategoryTheory.CategoryStruct.comp (Y.ofRestrict ⋯) g
Defined in
Mathlib.Geometry.RingedSpace.OpenImmersion
Cited by
0 results in Mathlib
Foundations
Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryAlgebraicGeometry.PresheafedSpace.IsOpenImmersion
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AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeft · cited by 3IsOpenImmersion.pullbackC…DFunLike.coe · cited by 62936DFunLike.coeCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.NatTrans.app · cited by 7406NatTrans.appCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Category.assoc · cited by 6433Category.assocCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homTopCat.carrier · cited by 3184TopCat.carrierOpposite.unop · cited by 2231Opposite.unopTopologicalSpace.Opens · cited by 2040TopologicalSpace.OpensIsOpenImmersion.pullback_cone…CITED BYCITES

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