Theorems · Theorem · category theory

CategoryTheory.Over.associator_hom_left_fst

∀ {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),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Over.Hom.left (CategoryTheory.MonoidalCategoryStruct.associator R S T).hom)
      (CategoryTheory.Limits.pullback.fst R.hom
        (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.fst S.hom T.hom) S.hom)) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Limits.pullback.fst (CategoryTheory.MonoidalCategoryStruct.tensorObj R S).hom T.hom)
      (CategoryTheory.Limits.pullback.fst R.hom S.hom)

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Over

Cited by

1 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacks