quotQuotMkₐ — Mathlib

English

The composition liftSupQuotQuotMk and quotLeftToQuotSupₐ examples show the compatibility of breaking and reassembling quotients with the algebra structure.

Русский

Композиции liftSupQuotQuotMk и quotLeftToQuotSupₐ демонстрируют совместимость разбиения и повторного составления квот с алгебраической структурой.

LaTeX

$$$liftSupQuotQuotMkₐ \circ quotLeftToQuotSupₐ = quotQuotSup Mk$$$

Lean4

/-- The composition of the algebra homomorphisms `A → (A / I)` and `(A / I) → (A / I) / J'`,
  where `J'` is the projection `J` in `A / I`. -/
def quotQuotMkₐ : A →ₐ[R] (A ⧸ I) ⧸ J.map (Quotient.mkₐ R I) :=
  AlgHom.mk (quotQuotMk I J) fun _ => rfl

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