Theorems · Theorem · category theory

DirectLimit.NonUnitalStarRing.hom_ext

∀ {ι : Type u_2} [inst : Preorder ι] {G : ι → Type u_3} {T : ⦃i j : ι⦄ → i ≤ j → Type u_6}
  {f : (x x_1 : ι) → (h : x ≤ x_1) → T h} [inst_1 : (i j : ι) → (h : i ≤ j) → FunLike (T h) (G i) (G j)]
  [inst_2 : DirectedSystem G fun x1 x2 x3 => ⇑(f x1 x2 x3)] [inst_3 : IsDirectedOrder ι]
  [inst_4 : (i : ι) → NonUnitalNonAssocSemiring (G i)]
  [inst_5 : ∀ (i j : ι) (h : i ≤ j), NonUnitalRingHomClass (T h) (G i) (G j)] [inst_6 : (i : ι) → StarRing (G i)]
  [inst_7 : ∀ (i j : ι) (h : i ≤ j), StarHomClass (T h) (G i) (G j)] [inst_8 : Nonempty ι] (P : Type u_7)
  [inst_9 : NonUnitalNonAssocSemiring P] [inst_10 : StarRing P] {g₁ g₂ : DirectLimit G f →⋆ₙ+* P},
  (∀ (i : ι), g₁.comp (DirectLimit.NonUnitalStarRing.of G f i) = g₂.comp (DirectLimit.NonUnitalStarRing.of G f i)) →
    g₁ = g₂

Defined in

Mathlib.Algebra.Colimit.DirectLimit

Cited by

1 results in Mathlib

Foundations

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

Assumes

PreorderFunLikeDirectedSystemIsDirectedOrderNonUnitalNonAssocSemiringNonUnitalRingHomClassStarRingStarHomClassNonemptyNonUnitalNonAssocSemiringStarRing