Theorems · Definition · category theory

TopModuleCat.ofHom

{R : Type u} →
  [inst : Ring R] →
    [inst_1 : TopologicalSpace R] →
      {X Y : Type v} →
        [inst_2 : AddCommGroup X] →
          [inst_3 : Module R X] →
            [inst_4 : TopologicalSpace X] →
              [inst_5 : ContinuousAdd X] →
                [inst_6 : ContinuousSMul R X] →
                  [inst_7 : AddCommGroup Y] →
                    [inst_8 : Module R Y] →
                      [inst_9 : TopologicalSpace Y] →
                        [inst_10 : ContinuousAdd Y] →
                          [inst_11 : ContinuousSMul R Y] → (X →L[R] Y) → (TopModuleCat.of R X ⟶ TopModuleCat.of R Y)

Construct a hom in TopModuleCat from a continuous linear map.

Defined in

Mathlib.Algebra.Category.ModuleCat.Topology.Basic

Cited by

4 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingTopologicalSpaceAddCommGroupModuleTopologicalSpaceContinuousAddContinuousSMulAddCommGroupModuleTopologicalSpaceContinuousAddContinuousSMul