Theorems · Definition · global analysis

smoothSheafCommRing.forgetStalk

{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)) →
                                              ↑((smoothSheafCommRing IM I M R).presheaf.stalk x) ≅
                                                (smoothSheaf IM I M R).presheaf.stalk x

Identify the stalk at a point of the sheaf-of-commutative-rings of functions from M to R (for R a smooth ring) with the stalk at that point of the corresponding sheaf of types.

Defined in

Mathlib.Geometry.Manifold.Sheaf.Smooth

Cited by

13 results in Mathlib

Foundations

Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpaceCommRingContMDiffRing