Theorems · Definition · category theory

CategoryTheory.Dial.associatorImpl

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasFiniteProducts C] →
      [inst_2 : CategoryTheory.Limits.HasPullbacks C] →
        (X Y Z : CategoryTheory.Dial C) → (X.tensorObjImpl Y).tensorObjImpl Z ≅ X.tensorObjImpl (Y.tensorObjImpl Z)

The associator for tensor, (X ⊗ Y) ⊗ Z ≅ X ⊗ (Y ⊗ Z) in Dial C.

Defined in

Mathlib.CategoryTheory.Dialectica.Monoidal

Cited by

4 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasFiniteProductsCategoryTheory.Limits.HasPullbacks