Theorems · Definition · category theory

CategoryTheory.Equivalence.mapContAction

{V : Type u_5} →
  {W : Type u_6} →
    [inst : CategoryTheory.Category.{v_2, u_5} V] →
      {FV : V → V → Type u_7} →
        {CV : V → Type u_8} →
          [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] →
                [inst_4 : CategoryTheory.Category.{v_3, u_6} W] →
                  {FW : W → W → Type u_9} →
                    {CW : W → Type u_10} →
                      [inst_5 : (X Y : W) → FunLike (FW X Y) (CW X) (CW Y)] →
                        [inst_6 : CategoryTheory.ConcreteCategory W FW] →
                          [inst_7 : CategoryTheory.HasForget₂ W TopCat] →
                            (G : Type u_11) →
                              [inst_8 : Monoid G] →
                                [inst_9 : TopologicalSpace G] →
                                  (E : V ≌ W) →
                                    (∀ (X : ContAction V G), ((E.functor.mapAction G).obj X.obj).IsContinuous) →
                                      (∀ (X : ContAction W G), ((E.inverse.mapAction G).obj X.obj).IsContinuous) →
                                        (ContAction V G ≌ ContAction W G)

Continuous version of Equivalence.mapAction.

Defined in

Mathlib.CategoryTheory.Action.Continuous

Cited by

2 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.HasForget₂CategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.HasForget₂MonoidTopologicalSpace