Theorems · Definition · logic and foundations

FirstOrder.Language.DirectLimit.of

(L : FirstOrder.Language) →
  (ι : Type v) →
    [inst : Preorder ι] →
      (G : ι → Type w) →
        [inst_1 : (i : ι) → L.Structure (G i)] →
          (f : (i j : ι) → i ≤ j → L.Embedding (G i) (G j)) →
            [inst_2 : IsDirectedOrder ι] →
              [inst_3 : DirectedSystem G fun i j h => ⇑(f i j h)] →
                [inst_4 : Nonempty ι] → (i : ι) → L.Embedding (G i) (FirstOrder.Language.DirectLimit G f)

The canonical map from a component to the direct limit.

Defined in

Mathlib.ModelTheory.DirectLimit

Cited by

17 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderFirstOrder.Language.StructureIsDirectedOrderDirectedSystemNonempty