Theorems · Theorem · category theory

CategoryTheory.Over.pullback_map_left

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ⟶ Y)
  [inst_1 : CategoryTheory.Limits.HasPullbacksAlong f] (g : CategoryTheory.Over Y) {h : CategoryTheory.Over Y}
  {k : g ⟶ h},
  ((CategoryTheory.Over.pullback f).map k).left =
    CategoryTheory.Limits.pullback.lift
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.fst g.hom f) (CategoryTheory.Over.Hom.left k))
      (CategoryTheory.Limits.pullback.snd g.hom f) ⋯

Defined in

Mathlib.CategoryTheory.Comma.Over.Pullback

Cited by

9 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacksAlong