Theorems · Theorem · commutative algebra

Ring.DirectLimit.ringEquiv_of

∀ {ι : Type u_1} [inst : Preorder ι] (G : ι → Type u_2) [inst_1 : (i : ι) → CommRing (G i)]
  (f' : (i j : ι) → i ≤ j → G i →+* G j) [inst_2 : DirectedSystem G fun i j h => ⇑(f' i j h)]
  [inst_3 : IsDirectedOrder ι] [inst_4 : Nonempty ι] {i : ι} {g : G i},
  (Ring.DirectLimit.ringEquiv G f') ((Ring.DirectLimit.of G (fun x1 x2 x3 => ⇑(f' x1 x2 x3)) i) g) = ⟦⟨i, g⟩⟧

Defined in

Mathlib.Algebra.Colimit.Ring

Cited by

1 results in Mathlib

Foundations

Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderCommRingDirectedSystemIsDirectedOrderNonempty