Theorems · Theorem · category theory

CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_fst

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasPullbacks C] {X Y : C}
  (f : X ⟶ Y) (A B : CategoryTheory.Over Y),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Over.Hom.left
        (CategoryTheory.CartesianMonoidalCategory.prodComparisonIso (CategoryTheory.Over.pullback f) A B).inv)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Limits.pullback.fst
          (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.fst A.hom B.hom) A.hom) f)
        (CategoryTheory.Limits.pullback.fst A.hom B.hom)) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Limits.pullback.fst (CategoryTheory.Limits.pullback.snd A.hom f)
        (CategoryTheory.Limits.pullback.snd B.hom f))
      (CategoryTheory.Limits.pullback.fst A.hom f)

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Over

Cited by

1 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacks