Theorems · Theorem · category theory

CategoryTheory.Limits.isPushout_map_codiagonal

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {X Y : C} [inst_1 : CategoryTheory.Limits.HasPushouts C]
  {S T : C} (f : T ⟶ X) (g : T ⟶ Y) (i : S ⟶ T),
  CategoryTheory.IsPushout
    (CategoryTheory.Limits.pushout.map i i (CategoryTheory.CategoryStruct.comp i f)
      (CategoryTheory.CategoryStruct.comp i g) f g (CategoryTheory.CategoryStruct.id S) ⋯ ⋯)
    (CategoryTheory.Limits.pushout.codiagonal i)
    (CategoryTheory.Limits.pushout.map (CategoryTheory.CategoryStruct.comp i f) (CategoryTheory.CategoryStruct.comp i g)
      f g (CategoryTheory.CategoryStruct.id X) (CategoryTheory.CategoryStruct.id Y) i ⋯ ⋯)
    (CategoryTheory.CategoryStruct.comp f (CategoryTheory.Limits.pushout.inl f g))

Given f : T ⟶ X, g : T ⟶ Y, and i : S ⟶ T, the diagram `` X ⨿ₛ Y ⟶ X ⨿ₜ Y ↑ ↑ | | | | T ⨿ₛ T ⟶ T `` is a pushout square.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Diagonal

Cited by

1 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPushouts