Theorems · Theorem · commutative algebra

QuotSMulTop.map_exact

∀ {R : Type u_2} [inst : CommRing R] (r : R) {M : Type u_1} {M' : Type u_3} {M'' : Type u_4} [inst_1 : AddCommGroup M]
  [inst_2 : Module R M] [inst_3 : AddCommGroup M'] [inst_4 : Module R M'] [inst_5 : AddCommGroup M'']
  [inst_6 : Module R M''] {f : M →ₗ[R] M'} {g : M' →ₗ[R] M''},
  Function.Exact ⇑f ⇑g → Function.Surjective ⇑g → Function.Exact ⇑((QuotSMulTop.map r) f) ⇑((QuotSMulTop.map r) g)

Defined in

Mathlib.RingTheory.QuotSMulTop

Cited by

1 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleAddCommGroupModule