Theorems · Definition · logic and foundations

FirstOrder.Language.DirectLimit

{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)) →
            [DirectedSystem G fun i j h => ⇑(f i j h)] → [IsDirectedOrder ι] → Type (max v w)

The direct limit of a directed system is the structures glued together along the embeddings.

Defined in

Mathlib.ModelTheory.DirectLimit

Cited by

23 results in Mathlib

Foundations

Depth 17 from the axioms · uses Quot.sound

Assumes

PreorderFirstOrder.Language.StructureDirectedSystemIsDirectedOrder