of_isLimit — Mathlib

English

Variant of hom_ext: equality of two CatCospanTransform morphisms is determined by equality on left/right components.

Русский

Вариант hom_ext: равенство двух гомоморфизмов CatCospanTransform определяется по соответствию левой и правой компонент.

LaTeX

$$Eq θ.left θ'.left → Eq θ.right θ'.right → Eq θ θ'$$

Lean4

/-- If `c` is a limiting pullback cone, then we have an `IsPullback c.fst c.snd f g`. -/
theorem of_isLimit {c : PullbackCone f g} (h : Limits.IsLimit c) : IsPullback c.fst c.snd f g :=
  { w := c.condition
    isLimit' := ⟨IsLimit.ofIsoLimit h (Limits.PullbackCone.ext (Iso.refl _) (by simp) (by simp))⟩ }

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