Theorems · Definition · category theory

Bimod.tensorBimod

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      [CategoryTheory.Limits.HasCoequalizers C] →
        [∀ (X : C),
              CategoryTheory.Limits.PreservesColimitsOfSize.{0, 0, v₁, v₁, u₁, u₁}
                (CategoryTheory.MonoidalCategory.tensorLeft X)] →
          [∀ (X : C),
                CategoryTheory.Limits.PreservesColimitsOfSize.{0, 0, v₁, v₁, u₁, u₁}
                  (CategoryTheory.MonoidalCategory.tensorRight X)] →
            {X Y Z : CategoryTheory.Mon C} → Bimod X Y → Bimod Y Z → Bimod X Z

Tensor product of two bimodule objects as a bimodule object.

Defined in

Mathlib.CategoryTheory.Monoidal.Bimod

Cited by

25 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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