Theorems · Definition · category theory

CategoryTheory.Limits.PushoutCocone.pasteVertFlip

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {Y₃ Y₂ Y₁ X₃ : C} →
      {g₂ : Y₃ ⟶ Y₂} →
        {g₁ : Y₂ ⟶ Y₁} →
          {i₃ : Y₃ ⟶ X₃} →
            (t₁ : CategoryTheory.Limits.PushoutCocone g₂ i₃) →
              {i₂ : Y₂ ⟶ t₁.pt} →
                (t₂ : CategoryTheory.Limits.PushoutCocone g₁ i₂) →
                  (hi₂ : i₂ = t₁.inl) → (t₁.pasteVert t₂ hi₂).flip ≅ t₁.flip.pasteHoriz t₂.flip hi₂

Pasting two pushout cocones vertically is isomorphic to the pushout cocone obtained by flipping them, pasting horizontally, and then flipping the result again.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.Category