Theorems · Theorem · category theory

CategoryTheory.IsPullback.map_fst_comp_fst_snd_comp_fst

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y Z U S : C} (f : X ⟶ S) (g : Y ⟶ S) (i : Z ⟶ S)
  [inst_1 : CategoryTheory.Limits.HasPullback i g] (h : U ⟶ CategoryTheory.Limits.pullback i g)
  [inst_2 : CategoryTheory.Limits.HasPullback f g]
  [inst_3 :
    CategoryTheory.Limits.HasPullback (CategoryTheory.Limits.pullback.snd f g)
      (CategoryTheory.CategoryStruct.comp h (CategoryTheory.Limits.pullback.snd i g))]
  [inst_4 : CategoryTheory.Limits.HasPullback f i],
  CategoryTheory.IsPullback
    (CategoryTheory.Limits.pullback.map (CategoryTheory.Limits.pullback.snd f g)
      (CategoryTheory.CategoryStruct.comp h (CategoryTheory.Limits.pullback.snd i g)) f i
      (CategoryTheory.Limits.pullback.fst f g)
      (CategoryTheory.CategoryStruct.comp h (CategoryTheory.Limits.pullback.fst i g)) g ⋯ ⋯)
    (CategoryTheory.Limits.pullback.snd (CategoryTheory.Limits.pullback.snd f g)
      (CategoryTheory.CategoryStruct.comp h (CategoryTheory.Limits.pullback.snd i g)))
    (CategoryTheory.Limits.pullback.snd f i)
    (CategoryTheory.CategoryStruct.comp h (CategoryTheory.Limits.pullback.fst i g))

This is a HasPullback variant of CategoryTheory.IsPullback.paste_twist_right

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

Cited by

0 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbackCategoryTheory.Limits.HasPullbackCategoryTheory.Limits.HasPullbackCategoryTheory.Limits.HasPullback