Theorems · Theorem · category theory

CategoryTheory.Over.associator_hom_left_fst_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasPullbacks C] {X : C}
  (R S T : CategoryTheory.Over X) {Z : C} (h : R.left ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Over.Hom.left (CategoryTheory.MonoidalCategoryStruct.associator R S T).hom)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Limits.pullback.fst R.hom
          (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.fst S.hom T.hom) S.hom))
        h) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Limits.pullback.fst (CategoryTheory.MonoidalCategoryStruct.tensorObj R S).hom T.hom)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.fst R.hom S.hom) h)

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Over

Cited by

0 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacks