Theorems · Theorem · global analysis

smoothSheafCommRing.forgetStalk_inv_comp_eval_apply

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {EM : Type u_2} [inst_1 : NormedAddCommGroup EM]
  [inst_2 : NormedSpace 𝕜 EM] {HM : Type u_3} [inst_3 : TopologicalSpace HM] (IM : ModelWithCorners 𝕜 EM HM)
  {E : Type u_4} [inst_4 : NormedAddCommGroup E] [inst_5 : NormedSpace 𝕜 E] {H : Type u_5} [inst_6 : TopologicalSpace H]
  (I : ModelWithCorners 𝕜 E H) (M : Type u) [inst_7 : TopologicalSpace M] [inst_8 : ChartedSpace HM M] (R : Type u)
  [inst_9 : TopologicalSpace R] [inst_10 : ChartedSpace H R] [inst_11 : CommRing R] [inst_12 : ContMDiffRing I (↑⊤) R]
  (x : ↑(TopCat.of M)) (x_1 : (smoothSheaf IM I M R).presheaf.stalk x),
  (CommRingCat.Hom.hom (smoothSheafCommRing.evalHom IM I M R x))
      ((CategoryTheory.ConcreteCategory.hom (smoothSheafCommRing.forgetStalk IM I M R x).inv) x_1) =
    (CategoryTheory.ConcreteCategory.hom (smoothSheaf.evalHom IM I R x)) x_1

Defined in

Mathlib.Geometry.Manifold.Sheaf.Smooth

Cited by

1 results in Mathlib

Foundations

Depth 233 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpaceCommRingContMDiffRing