whiskerEquiv — Mathlib

English

The optimal isomorphism between sigma-objects preserves the colimit structure under whiskering by an equivalence.

Русский

Оптимальное изоморфизм между сигма-объектами сохраняет структуру колимита при взвешивании эквивалентностью.

LaTeX

$$$\\text{WhiskerEquiv isColimit}$$$

Lean4

/-- Two coproducts which differ by an equivalence in the indexing type,
and up to isomorphism in the factors, are isomorphic.
-/
@[simps]
def whiskerEquiv {J K : Type*} {f : J → C} {g : K → C} (e : J ≃ K) (w : ∀ j, g (e j) ≅ f j) [HasCoproduct f]
    [HasCoproduct g] : ∐ f ≅ ∐ g where
  hom := Sigma.map' e fun j => (w j).inv
  inv := Sigma.map' e.symm fun k => eqToHom (by simp) ≫ (w (e.symm k)).hom

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