Theorems · Theorem · linear algebra

LinearMap.coprodEquiv_symm_apply

∀ {R : Type u} {M : Type v} {M₂ : Type w} {M₃ : Type y} (S : Type u_3) [inst : Semiring R] [inst_1 : Semiring S]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : AddCommMonoid M₃] [inst_5 : Module R M]
  [inst_6 : Module R M₂] [inst_7 : Module R M₃] [inst_8 : Module S M₃] [inst_9 : SMulCommClass R S M₃]
  (f : M × M₂ →ₗ[R] M₃), (LinearMap.coprodEquiv S).symm f = (f ∘ₗ LinearMap.inl R M M₂, f ∘ₗ LinearMap.inr R M M₂)

Defined in

Mathlib.LinearAlgebra.Prod

Cited by

0 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleModuleSMulCommClass