Theorems · Definition · Lie groups

ProfiniteGrp.ofHom

{X Y : Type u} →
  [inst : Group X] →
    [inst_1 : TopologicalSpace X] →
      [inst_2 : IsTopologicalGroup X] →
        [inst_3 : CompactSpace X] →
          [inst_4 : TotallyDisconnectedSpace X] →
            [inst_5 : Group Y] →
              [inst_6 : TopologicalSpace Y] →
                [inst_7 : IsTopologicalGroup Y] →
                  [inst_8 : CompactSpace Y] →
                    [inst_9 : TotallyDisconnectedSpace Y] → (X →ₜ* Y) → (ProfiniteGrp.of X ⟶ ProfiniteGrp.of Y)

Typecheck a ContinuousMonoidHom as a morphism in ProfiniteGrp.

Defined in

Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic

Cited by

5 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupTopologicalSpaceIsTopologicalGroupCompactSpaceTotallyDisconnectedSpaceGroupTopologicalSpaceIsTopologicalGroupCompactSpaceTotallyDisconnectedSpace