Theorems · Definition · category theory

CategoryTheory.Mod.comap

{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] →
            {A B : C} →
              [inst_4 : CategoryTheory.MonObj A] →
                [inst_5 : CategoryTheory.MonObj B] →
                  (f : A ⟶ B) →
                    [CategoryTheory.IsMonHom f] →
                      CategoryTheory.Functor (CategoryTheory.Mod D B) (CategoryTheory.Mod D A)

A morphism of monoid objects induces a "restriction" or "comap" functor between the categories of module objects.

Defined in

Mathlib.CategoryTheory.Monoidal.Mod

Cited by

3 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategory.MonoidalLeftActionCategoryTheory.MonObjCategoryTheory.MonObjCategoryTheory.IsMonHom