Theorems · Definition · linear algebra

Finsupp.lcongr

{M : Type u_2} →
  {N : Type u_3} →
    {R : Type u_5} →
      {R₂ : Type u_6} →
        [inst : Semiring R] →
          [inst_1 : Semiring R₂] →
            [inst_2 : AddCommMonoid M] →
              [inst_3 : Module R M] →
                [inst_4 : AddCommMonoid N] →
                  [inst_5 : Module R₂ N] →
                    {σ : R →+* R₂} →
                      {σ_inv : R₂ →+* R} →
                        [inst_6 : RingHomInvPair σ σ_inv] →
                          [inst_7 : RingHomInvPair σ_inv σ] →
                            {ι : Type u_9} → {κ : Type u_10} → ι ≃ κ → (M ≃ₛₗ[σ] N) → (ι →₀ M) ≃ₛₗ[σ] κ →₀ N

An equivalence of domain and a linear equivalence of codomain induce a linear equivalence of the corresponding finitely supported functions.

Defined in

Mathlib.LinearAlgebra.Finsupp.LSum

Cited by

22 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringAddCommMonoidModuleAddCommMonoidModuleRingHomInvPairRingHomInvPair