Theorems · Theorem · global analysis

ContMDiff.smoothSheafHom_hom_app_coe

Deprecated since 2026-04-06Use ContMDiff.smoothSheafHom_hom_app_hom instead.

∀ {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] {N : Type u}
  [inst_9 : TopologicalSpace N] [inst_10 : ChartedSpace H N] {EP : Type u_7} [inst_11 : NormedAddCommGroup EP]
  [inst_12 : NormedSpace 𝕜 EP] {HP : Type u_8} [inst_13 : TopologicalSpace HP] (IP : ModelWithCorners 𝕜 EP HP)
  (P : Type u) [inst_14 : TopologicalSpace P] [inst_15 : ChartedSpace HP P] (f : M → P) (hf : ContMDiff IM IP (↑⊤) f)
  (U : (TopologicalSpace.Opens ↑(TopCat.of P))ᵒᵖ),
  CategoryTheory.ConcreteCategory.hom ((ContMDiff.smoothSheafHom IP P f hf).hom.app U) =
    { toFun := fun g => ⟨↑g ∘ (↑(Opposite.unop U)).restrictPreimage f, ⋯⟩ }

Alias of ContMDiff.smoothSheafHom_hom_app_hom.

Defined in

Mathlib.Geometry.Manifold.Sheaf.Smooth

Cited by

0 results in Mathlib

Foundations

Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace