Mathlib Map

Theorems · Definition · category theory

CategoryTheory.ModObj.smul

{C : Type u₁} →
  {inst : CategoryTheory.Category.{v₁, u₁} C} →
    {inst_1 : CategoryTheory.MonoidalCategory C} →
      {D : Type u₂} →
        {inst_2 : CategoryTheory.Category.{v₂, u₂} D} →
          {inst_3 : CategoryTheory.MonoidalCategory.MonoidalLeftAction C D} →
            {M : C} →
              {inst_4 : CategoryTheory.MonObj M} →
                {X : D} →
                  [self : CategoryTheory.ModObj M X] →
                    CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionObj M X ⟶ X

The action map

Defined in
Mathlib.CategoryTheory.Monoidal.Mod
Cited by
36 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
CategoryTheory.ModObj
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.ModObj.leftSMul · cited by 8ModObj.leftSMulCategoryTheory.Mod.scalarRestriction · cited by 5Mod.scalarRestrictionCategoryTheory.IsModHom.smul_hom · cited by 4IsModHom.smul_homCategoryTheory.ModObj.mul_smul · cited by 4ModObj.mul_smulCategoryTheory.ModObj.leftSMul_fst · cited by 3ModObj.leftSMul_fstCategoryTheory.ModObj.leftSMul_snd · cited by 3ModObj.leftSMul_sndCategoryTheory.ModObj.mul_smul_self · cited by 2ModObj.mul_smul_selfCategoryTheory.ModObj.one_smul · cited by 2ModObj.one_smulCategoryTheory.Hom.smul_def · cited by 1Hom.smul_defCategoryTheory.Mod.assoc_flip · cited by 1Mod.assoc_flipCategoryTheory.IsModHom.map_smul · cited by 1IsModHom.map_smulCategoryTheory.Mod.scalarRestriction_hom · cited by 1Mod.scalarRestriction_homCategoryTheory.Mod.scalarRestriction_smul · cited by 1Mod.scalarRestriction_smulCategoryTheory.ModObj.ext · cited by 1ModObj.extCategoryTheory.ModObj.lift_leftSMul · cited by 1ModObj.lift_leftSMulCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.MonoidalCategory.MonoidalLeftAction · cited by 215MonoidalCategory.Monoidal…CategoryTheory.MonObj · cited by 199CategoryTheory.MonObjCategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionObj · cited by 185MonoidalLeftActionStruct.…CategoryTheory.ModObj · cited by 38CategoryTheory.ModObjModObj.smulCITED BYCITES

Cites7

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

Cited by45

Results whose statement or proof uses this declaration.