Theorems · Theorem · category theory

CategoryTheory.Functor.mapContActionComp_hom

∀ {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]
  {T : Type u_12} [inst_10 : CategoryTheory.Category.{v_4, u_12} T] {FT : T → T → Type u_13} {CT : T → Type u_14}
  [inst_11 : (X Y : T) → FunLike (FT X Y) (CT X) (CT Y)] [inst_12 : CategoryTheory.ConcreteCategory T FT]
  [inst_13 : CategoryTheory.HasForget₂ T TopCat] (F : CategoryTheory.Functor V W)
  (H : ∀ (X : ContAction V G), ((F.mapAction G).obj X.obj).IsContinuous) (F' : CategoryTheory.Functor W T)
  (H' : ∀ (X : ContAction W G), ((F'.mapAction G).obj X.obj).IsContinuous),
  (CategoryTheory.Functor.mapContActionComp G F H F' H').hom =
    { app := fun X => CategoryTheory.CategoryStruct.id ((CategoryTheory.Functor.mapContAction G (F.comp F') ⋯).obj X),
      naturality := ⋯ }

Defined in

Mathlib.CategoryTheory.Action.Continuous

Cited by

0 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.HasForget₂CategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.HasForget₂MonoidTopologicalSpaceCategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.HasForget₂