Theorems · Theorem · functional analysis

ContinuousLinearMap.coprod_comp_prodComm

∀ {R : Type u_1} {M : Type u_2} {M₂ : Type u_3} {M₃ : Type u_4} [inst : TopologicalSpace M]
  [inst_1 : TopologicalSpace M₂] [inst_2 : TopologicalSpace M₃] [inst_3 : Semiring R] [inst_4 : AddCommMonoid M]
  [inst_5 : Module R M] [inst_6 : AddCommMonoid M₂] [inst_7 : Module R M₂] [inst_8 : AddCommMonoid M₃]
  [inst_9 : Module R M₃] [inst_10 : ContinuousAdd M] (f : M₂ →L[R] M) (g : M₃ →L[R] M),
  f.coprod g ∘SL ↑(ContinuousLinearEquiv.prodComm R M₃ M₂) = g.coprod f

Composition of a map on a product with the exchange of the product factors

Defined in

Mathlib.Topology.Algebra.Module.Equiv

Cited by

0 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceSemiringAddCommMonoidModuleAddCommMonoidModuleAddCommMonoidModuleContinuousAdd