Theorems · Definition · category theory

CategoryTheory.IsModHom.mulActionHom

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      {M : C} →
        [inst_2 : CategoryTheory.MonObj M] →
          {X : C} →
            [inst_3 : CategoryTheory.ModObj M X] →
              {Y : C} →
                [inst_4 : CategoryTheory.ModObj M Y] →
                  (f : X ⟶ Y) → [CategoryTheory.IsModHom M f] → (Z : C) → (Z ⟶ X) →ₑ[id] Z ⟶ Y

An M-equivariant morphism induces an equivariant function on hom types.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Mod

Cited by

1 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.MonObjCategoryTheory.ModObjCategoryTheory.ModObjCategoryTheory.IsModHom