Theorems · Definition · ring theory

DirectSum.lequivCongrLeft

(R : Type u) →
  [inst : Semiring R] →
    {ι : Type v} →
      {M : ι → Type w} →
        [inst_1 : (i : ι) → AddCommMonoid (M i)] →
          [inst_2 : (i : ι) → Module R (M i)] →
            {κ : Type u_1} → (h : ι ≃ κ) → (DirectSum ι fun i => M i) ≃ₗ[R] DirectSum κ fun k => M (h.symm k)

Reindexing terms of a direct sum is linear.

Defined in

Mathlib.Algebra.DirectSum.Module

Cited by

7 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule