weakEquivalence_of_precomp_of_fac

English

In the given setting, trivial cofibrations are closed under retracts.

Русский

В заданной обстановке тривиальные кофибрации замыкаются под retracts.

LaTeX

$$$\operatorname{IsStableUnderRetracts}\big(\operatorname{trivialCofibrations}(C)\big)$$$

Lean4

theorem weakEquivalence_of_precomp_of_fac (fac : f ≫ g = fg) [WeakEquivalence f] [WeakEquivalence fg] :
    WeakEquivalence g := by
  subst fac
  exact weakEquivalence_of_precomp f g

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