isUniversalPostcomp₁Equiv — Mathlib

English

There is an equivalence between universality of a left extension ex and the universality of its precomposition ex.precomp along G.

Русский

Существует эквивалентность между universality левого расширения ex и universality его предрасширения ex.precomp вдоль G.

LaTeX

$$ex.IsUniversal ≃ ((LeftExtension.precomp L F G).obj ex).IsUniversal$$

Lean4

/-- Given an isomorphism `e : L ⋙ G ≅ L'`, a right extension of `F` along `L'` is universal
iff the corresponding right extension of `L` along `L` is. -/
noncomputable def isUniversalPostcomp₁Equiv (ex : RightExtension L' F) :
    ex.IsUniversal ≃ ((RightExtension.postcomp₁ G e.hom F).obj ex).IsUniversal := by
  apply IsTerminal.isTerminalIffObj (RightExtension.postcomp₁ G e.hom F)

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