Theorems · Theorem · commutative algebra

Ring.DirectLimit.of_f

∀ {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} {i j : ι} (hij : i ≤ j) (x : G i),
  (Ring.DirectLimit.of G f j) (f i j hij x) = (Ring.DirectLimit.of G f i) x

Defined in

Mathlib.Algebra.Colimit.Ring

Cited by

2 results in Mathlib

Foundations

Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderCommRing