Theorems · Definition · category theory

ContAction.resEquiv

(V : Type u_1) →
  [inst : CategoryTheory.Category.{v_1, u_1} V] →
    {FV : V → V → Type u_2} →
      {CV : V → Type u_3} →
        [inst_1 : (X Y : V) → FunLike (FV X Y) (CV X) (CV Y)] →
          [inst_2 : CategoryTheory.ConcreteCategory V FV] →
            [inst_3 : CategoryTheory.HasForget₂ V TopCat] →
              {G : Type u_4} →
                [inst_4 : Monoid G] →
                  [inst_5 : TopologicalSpace G] →
                    {H : Type u_5} →
                      [inst_6 : Monoid H] → [inst_7 : TopologicalSpace H] → G ≃ₜ* H → (ContAction V H ≌ ContAction V G)

Restriction of scalars along a topological monoid isomorphism induces an equivalence of categories.

Defined in

Mathlib.CategoryTheory.Action.Continuous

Cited by

2 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.HasForget₂MonoidTopologicalSpaceMonoidTopologicalSpace