Theorems · Definition · category theory

CategoryTheory.IsPullback.isLimit

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {P X Y Z : C} →
      {fst : P ⟶ X} →
        {snd : P ⟶ Y} →
          {f : X ⟶ Z} → {g : Y ⟶ Z} → (h : CategoryTheory.IsPullback fst snd f g) → CategoryTheory.Limits.IsLimit h.cone

The cone obtained from IsPullback fst snd f g is a limit cone.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs

Cited by

47 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category