Theorems · Definition · category theory

Bimod.AssociatorBimod.homAux

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      [inst_2 : CategoryTheory.Limits.HasCoequalizers C] →
        [inst_3 :
            ∀ (X : C),
              CategoryTheory.Limits.PreservesColimitsOfSize.{0, 0, v₁, v₁, u₁, u₁}
                (CategoryTheory.MonoidalCategory.tensorLeft X)] →
          [inst_4 :
              ∀ (X : C),
                CategoryTheory.Limits.PreservesColimitsOfSize.{0, 0, v₁, v₁, u₁, u₁}
                  (CategoryTheory.MonoidalCategory.tensorRight X)] →
            {R S T U : CategoryTheory.Mon C} →
              (P : Bimod R S) →
                (Q : Bimod S T) →
                  (L : Bimod T U) →
                    CategoryTheory.MonoidalCategoryStruct.tensorObj (P.tensorBimod Q).X L.X ⟶
                      (P.tensorBimod (Q.tensorBimod L)).X

An auxiliary morphism for the definition of the underlying morphism of the forward component of the associator isomorphism.

Defined in

Mathlib.CategoryTheory.Monoidal.Bimod

Cited by

5 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Limits.HasCoequalizersCategoryTheory.Limits.PreservesColimitsOfSizeCategoryTheory.Limits.PreservesColimitsOfSize