Theorems · Definition · logic and foundations

FirstOrder.Language.Hom.codRestrict

{L : FirstOrder.Language} →
  {M : Type w} →
    {N : Type u_1} →
      [inst : L.Structure M] →
        [inst_1 : L.Structure N] → (p : L.Substructure N) → (f : L.Hom M N) → (∀ (c : M), f c ∈ p) → L.Hom M ↥p

A first-order hom f : M → N whose values lie in a substructure p ⊆ N can be restricted to a hom M → p.

Defined in

Mathlib.ModelTheory.Substructures

Cited by

4 results in Mathlib

Foundations

Depth 19 from the axioms · uses no axioms

Assumes

FirstOrder.Language.StructureFirstOrder.Language.Structure