English
Coherence relations for Mod_.assoc_flip with various module morphisms highlight associativity coherence.
Русский
Когерентные отношения Mod_.assoc_flip с различными мороморфизмами модуля подчёркивают когерентность ассоциатора.
LaTeX
$$$\\text{Mod_.assoc_flip}$$$
Lean4
/-- If `g : M ⟶ N` is a `B`-linear morphisms of `B`-modules, then it induces an
`A`-linear morphism when `M` and `N` have an `A`-module structure obtained
by restricting scalars along a monoid morphism `A ⟶ B`. -/
theorem scalarRestriction_hom (M N : D) [ModObj B M] [ModObj B N] (g : M ⟶ N) [IsMod_Hom B g] :
letI := scalarRestriction f M
letI := scalarRestriction f N
IsMod_Hom A g :=
letI := scalarRestriction f M
letI := scalarRestriction f N
{
smul_hom := by
dsimp
slice_rhs 1 2 => rw [action_exchange]
slice_rhs 2 3 => rw [← IsMod_Hom.smul_hom]
rw [Category.assoc] }
