Mathlib Map

Theorems Ā· Definition Ā· global analysis

smoothSheafAddCommGroup

{š•œ : Type u_1} ā†’
  [inst : NontriviallyNormedField š•œ] ā†’
    {EM : Type u_2} ā†’
      [inst_1 : NormedAddCommGroup EM] ā†’
        [inst_2 : NormedSpace š•œ EM] ā†’
          {HM : Type u_3} ā†’
            [inst_3 : TopologicalSpace HM] ā†’
              ModelWithCorners š•œ EM HM ā†’
                {E : Type u_4} ā†’
                  [inst_4 : NormedAddCommGroup E] ā†’
                    [inst_5 : NormedSpace š•œ E] ā†’
                      {H : Type u_5} ā†’
                        [inst_6 : TopologicalSpace H] ā†’
                          (I : ModelWithCorners š•œ E H) ā†’
                            (M : Type u) ā†’
                              [inst_7 : TopologicalSpace M] ā†’
                                [ChartedSpace HM M] ā†’
                                  (A : Type u) ā†’
                                    [inst_9 : TopologicalSpace A] ā†’
                                      [inst_10 : ChartedSpace H A] ā†’
                                        [inst_11 : AddCommGroup A] ā†’
                                          [LieAddGroup I (ā†‘āŠ¤) A] ā†’ TopCat.Sheaf AddCommGrpCat (TopCat.of M)

The sheaf of smooth functions from M to A, for A an abelian additive Lie group, as a sheaf of abelian additive groups.

Defined in
Mathlib.Geometry.Manifold.Sheaf.Smooth
Cited by
0 results in Mathlib
Foundations
Depth 221 from the axioms Ā· uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpaceAddCommGroupLieAddGroup
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

smoothSheafAddCommGroup.compLeft Ā· cited by 0smoothSheafAddCommGroup.cā€¦TopologicalSpace Ā· cited by 24529TopologicalSpaceNormedAddCommGroup Ā· cited by 15752NormedAddCommGroupAddCommGroup Ā· cited by 12871AddCommGroupNormedSpace Ā· cited by 12499NormedSpaceTop.top Ā· cited by 9680Top.topNontriviallyNormedField Ā· cited by 8742NontriviallyNormedFieldENat Ā· cited by 4985ENatModelWithCorners Ā· cited by 2462ModelWithCornersChartedSpace Ā· cited by 2397ChartedSpaceWithTop.some Ā· cited by 1128WithTop.someAddCommGrpCat Ā· cited by 462AddCommGrpCatTopCat.Sheaf Ā· cited by 73TopCat.SheafLieAddGroup Ā· cited by 22LieAddGroupsmoothPresheafAddCommGroup Ā· cited by 0smoothPresheafAddCommGroupsmoothSheafAddCommGroupCITED BYCITES

Cites14

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.