Mathlib Map

Theorems · Definition · category theory

CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionUnitIso

{C : Type u_1} →
  {D : Type u_2} →
    {inst : CategoryTheory.Category.{v_1, u_1} C} →
      {inst_1 : CategoryTheory.Category.{v_2, u_2} D} →
        {inst_2 : CategoryTheory.MonoidalCategoryStruct C} →
          [self : CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct C D] →
            (d : D) →
              CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionObj
                  (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) d ≅
                d

The structural isomorphism between 𝟙_ C ⊙ₗ d and d.

Defined in
Mathlib.CategoryTheory.Monoidal.Action.Basic
Cited by
39 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitIso_hom_naturality · cited by 3MonoidalLeftAction.action…CategoryTheory.ModObj.one_smul · cited by 2ModObj.one_smulCategoryTheory.Functor.OplaxLeftLinear.δₗ_unitality_inv · cited by 2OplaxLeftLinear.δₗ_unital…CategoryTheory.AddModObj.zero_vadd · cited by 2AddModObj.zero_vaddCategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitNatIso · cited by 2MonoidalLeftAction.action…CategoryTheory.Functor.LaxLeftLinear.μₗ_unitality · cited by 2LaxLeftLinear.μₗ_unitalityCategoryTheory.MonoidalCategory.MonoidalLeftAction.leftUnitor_actionHom · cited by 1MonoidalLeftAction.leftUn…CategoryTheory.MonoidalCategory.MonoidalLeftAction.rightUnitor_actionHom · cited by 1MonoidalLeftAction.rightU…CategoryTheory.MonoidalCategory.MonoidalLeftAction.unit_actionHomRight · cited by 1MonoidalLeftAction.unit_a…CategoryTheory.ModObj.casesOn · cited by 1ModObj.casesOnCategoryTheory.ModObj.ext · cited by 1ModObj.extCategoryTheory.Functor.OplaxLeftLinear.δₗ_unitality_hom · cited by 1OplaxLeftLinear.δₗ_unital…CategoryTheory.AddModObj.casesOn · cited by 1AddModObj.casesOnCategoryTheory.AddModObj.ext · cited by 1AddModObj.extCategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitIso_inv_naturality · cited by 1MonoidalLeftAction.action…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.MonoidalCategoryStruct.tensorUnit · cited by 1384MonoidalCategoryStruct.te…CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionObj · cited by 185MonoidalLeftActionStruct.…CategoryTheory.MonoidalCategoryStruct · cited by 26CategoryTheory.MonoidalCa…CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct · cited by 0MonoidalCategory.Monoidal…MonoidalLeftActionStruct.acti…CITED BYCITES

Cites6

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

Cited by65

Results whose statement or proof uses this declaration.