Theorems · Theorem · ring theory

DirectSum.mker_map

∀ {ι : Type v} {M : ι → Type w} [inst : (i : ι) → AddCommMonoid (M i)] {N : ι → Type u_1}
  [inst_1 : (i : ι) → AddCommMonoid (N i)] (f : (i : ι) → M i →+ N i),
  AddMonoidHom.mker (DirectSum.map f) =
    AddSubmonoid.comap (DirectSum.coeFnAddMonoidHom M) (AddSubmonoid.pi Set.univ fun i => AddMonoidHom.mker (f i))

Defined in

Mathlib.Algebra.DirectSum.Module

Cited by

0 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidAddCommMonoid