Σi ��Σj )(i<j)∈(I,≤) be a directed diagram of quasi-representable signature morphisms and let ( Σi be its colimit. We fix arbitrary i ∈ |I| and show that θi is quasi-representable. hi Let M↾θ �� i Ni be a Σi-homomorphism for some Σ-model M. For each j ∈ I (0)