Let XZY be a diagram of topological spaces and continuous functions. Describe a topological space A which has the following two properties: (1) there exist continuous maps : A X and 7: A Y such that fon = go , and (2) if A', is any other topological space satisfying (1) (so admitting continuous maps ': A' X and ': A' Y such that fo = go ), then there exists a continuous map A' A such that T = ol.