Theorems · Definition · linear algebra

LinearMap.coprod

{R : Type u} →
  {M : Type v} →
    {M₂ : Type w} →
      {M₃ : Type y} →
        [inst : Semiring R] →
          [inst_1 : AddCommMonoid M] →
            [inst_2 : AddCommMonoid M₂] →
              [inst_3 : AddCommMonoid M₃] →
                [inst_4 : Module R M] →
                  [inst_5 : Module R M₂] → [inst_6 : Module R M₃] → (M →ₗ[R] M₃) → (M₂ →ₗ[R] M₃) → M × M₂ →ₗ[R] M₃

The coprod function x : M × M₂ ↦ f x.1 + g x.2 is a linear map.

Defined in

Mathlib.LinearAlgebra.Prod

Cited by

38 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Quot.sound

Assumes

SemiringAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModule