Theorems · Theorem · algebraic geometry

ChartedSpace.locallyRingedSpace_comp

∀ {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]
  {EP : Type u_5} [inst_11 : NormedAddCommGroup EP] [inst_12 : NormedSpace 𝕜 EP] {HP : Type u_6}
  [inst_13 : TopologicalSpace HP] (IP : ModelWithCorners 𝕜 EP HP) {P : Type u} [inst_14 : TopologicalSpace P]
  [inst_15 : ChartedSpace HP P] {f : M → N} (hf : ContMDiff IM IN (↑⊤) f) {g : N → P} (hg : ContMDiff IN IP (↑⊤) g),
  ChartedSpace.locallyRingedSpaceMap (g ∘ f) ⋯ =
    CategoryTheory.CategoryStruct.comp (ChartedSpace.locallyRingedSpaceMap f hf)
      (ChartedSpace.locallyRingedSpaceMap g hg)

Defined in

Mathlib.Geometry.Manifold.Sheaf.LocallyRingedSpace

Cited by

0 results in Mathlib

Foundations

Depth 243 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace