Theorems · Theorem · algebraic geometry

ChartedSpace.stalkMap_locallyRingedSpaceMap_evalHom_assoc

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {EM : Type u_1} [inst_1 : NormedAddCommGroup EM]
  [inst_2 : NormedSpace 𝕜 EM] {HM : Type u_2} [inst_3 : TopologicalSpace HM] {IM : ModelWithCorners 𝕜 EM HM}
  {M : Type u} [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace HM M] {EN : Type u_3}
  [inst_6 : NormedAddCommGroup EN] [inst_7 : NormedSpace 𝕜 EN] {HN : Type u_4} [inst_8 : TopologicalSpace HN]
  {IN : ModelWithCorners 𝕜 EN HN} {N : Type u} [inst_9 : TopologicalSpace N] [inst_10 : ChartedSpace HN N] (f : M → N)
  (hf : ContMDiff IM IN (↑⊤) f) (x : M) {Z : CommRingCat} (h : CommRingCat.of 𝕜 ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (AlgebraicGeometry.LocallyRingedSpace.Hom.stalkMap (ChartedSpace.locallyRingedSpaceMap f hf) x)
      (CategoryTheory.CategoryStruct.comp (smoothSheafCommRing.evalHom IM (modelWithCornersSelf 𝕜 𝕜) M 𝕜 x) h) =
    CategoryTheory.CategoryStruct.comp (smoothSheafCommRing.evalHom IN (modelWithCornersSelf 𝕜 𝕜) N 𝕜 (f x)) h

Defined in

Mathlib.Geometry.Manifold.Sheaf.LocallyRingedSpace

Cited by

0 results in Mathlib

Foundations

Depth 244 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace