Analysis of information sources in references of the Wikipedia article "Library of Celsus" in English language version.
...statues (lost except for their bases) were probably of Celsus, consul in A.D. 92, and his son Aquila, consul in A.D. 110. A cuirass statue stood in the central niche of the upper storey. Its identification oscillates between Tiberius Julius Celsus Polemaeanus, who is buried in a sarcophagus under the library, and Tiberius Julius Aquila Polemaeanus, who completed the building for his father
Apart from the public buildings for which such benefactors paid—the library at Ephesos, for example, recently reconstructed, built by Tiberius Iulius Aquila Polmaeanus in 110–20 in honour of his father Tiberius Iulius Celsus Polemaeanus, one of the earliest men of purely Greek origin to become a Roman consul.
After all, the library was simultaneously the sepulchral monument of Celsus and the crypt contained his sarcophagus. The very idea of honouring his memory by erecting a public library above his grave need not have been the original conception of Tiberius Iulius Aquila the founder of the library.