Theorems · Theorem · commutative algebra

AdicCompletion.map_comp_apply

∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  {N : Type u_3} [inst_3 : AddCommGroup N] [inst_4 : Module R N] {P : Type u_4} [inst_5 : AddCommGroup P]
  [inst_6 : Module R P] (f : M →ₗ[R] N) (g : N →ₗ[R] P) (x : AdicCompletion I M),
  (AdicCompletion.map I g) ((AdicCompletion.map I f) x) = (AdicCompletion.map I (g ∘ₗ f)) x

Defined in

Mathlib.RingTheory.AdicCompletion.Functoriality

Cited by

1 results in Mathlib

Foundations

Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleAddCommGroupModule