Theorems · Definition · category theory

Action.FunctorCategoryEquivalence.unitIso

{V : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} V] →
    {G : Type u_2} →
      [inst_1 : Monoid G] →
        CategoryTheory.Functor.id (Action V G) ≅
          Action.FunctorCategoryEquivalence.functor.comp Action.FunctorCategoryEquivalence.inverse

Auxiliary definition for functorCategoryEquivalence.

Defined in: Mathlib.CategoryTheory.Action.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category Monoid

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites15

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functor.objproof · cited by 19,642
CategoryTheory.Functorstatement · cited by 16,252
CategoryTheory.Functor.compstatement · cited by 6,529
CategoryTheory.Isostatement · cited by 3,963
Monoidstatement and proof · cited by 3,887
CategoryTheory.Functor.idstatement and proof · cited by 3,333
CategoryTheory.Iso.reflproof · cited by 727
Actionstatement and proof · cited by 206
CategoryTheory.NatIso.ofComponentsproof · cited by 178
Action.Vproof · cited by 176
CategoryTheory.SingleObjstatement · cited by 88

Cited by4

Results whose statement or proof uses this declaration.

Action.functorCategoryEquivalenceproof · cited by 15
Action.FunctorCategoryEquivalence.unitIso_hom_app_homstatement and proof · cited by 0
Action.FunctorCategoryEquivalence.unitIso_inv_app_homstatement and proof · cited by 0
Action.functorCategoryEquivalence_unitIsostatement · cited by 0