Theorems · Definition · category theory

CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHom

{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] →
            {c c' : C} →
              {d d' : D} →
                (c ⟶ c') →
                  (d ⟶ d') →
                    (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionObj c d ⟶
                      CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionObj c' d')

The action of a pair of maps f : c ⟶ c' and d ⟶ d'. By default, this is defined in terms of actionHomLeft and actionHomRight.

Defined in

Mathlib.CategoryTheory.Monoidal.Action.Basic

Cited by

31 results in Mathlib

Foundations

Depth 4 from the axioms · uses no axioms

Assumes

CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct