Theorems · Theorem · category theory

DirectLimit.Module.of_apply

∀ (R : Type u_1) (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 : Semiring R]
  [inst_5 : (i : ι) → AddCommMonoid (G i)] [inst_6 : (i : ι) → Module R (G i)]
  [inst_7 : ∀ (i j : ι) (h : i ≤ j), LinearMapClass (T h) R (G i) (G j)] [inst_8 : Nonempty ι] (i : ι) (x : G i),
  (DirectLimit.Module.of R ι G f i) x = ⟦⟨i, x⟩⟧

Defined in

Mathlib.Algebra.Colimit.DirectLimit

Cited by

1 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderFunLikeDirectedSystemIsDirectedOrderSemiringAddCommMonoidModuleLinearMapClassNonempty