Module biproducts with a universe-polymorphic index #
Mathlib's explicit ModuleCat.biproductIsoPi specializes its finite index to
Type. This variant uses the already universe-polymorphic product cone.
noncomputable def
MagnitudeConjecture.ModuleCat.biproductIsoPi
{R : Type u}
[Ring R]
{J : Type w}
(f : J → ModuleCat R)
[Finite J]
:
⨁ f ≅ ModuleCat.of R ((j : J) → ↑(f j))
A finite categorical biproduct of modules is the dependent function module, with no restriction on the universe of the finite index.