Theorems · Theorem · category theory

ModuleCat.ExtendScalars.map_tmul

∀ {R : Type u₁} {S : Type u₂} [inst : CommRing R] [inst_1 : CommRing S] (f : R →+* S) {M M' : ModuleCat R} (g : M ⟶ M')
  (s : S) (m : ↑M),
  (CategoryTheory.ConcreteCategory.hom ((ModuleCat.extendScalars f).map g)) (s ⊗ₜ[R] m) =
    s ⊗ₜ[R] (CategoryTheory.ConcreteCategory.hom g) m

Defined in

Mathlib.Algebra.Category.ModuleCat.ChangeOfRings

Cited by

2 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRing