It can be argued that the material in Ephesians 4-6 and Colossians 3-4 reflect an early form of apostolic teaching or catechism material. The terms kerygma and didache are used to distinguish between two types of apostolic message. Kerygma is the “preaching” material of the gospel for sinners (Christ’s death and resurrection), while didache is the teaching material aimed at the person that has already accepted this message and is concerned with the living out of that message in terms of ethical behavior.
This may imply some pre-existing documents that eventually are used in the production of the New Testament books, although these types of materials also circulated orally. The kerygma material, for example, may include 1 Corinthians 15:3-5 or Phil 2:5-11. But this is not to say that there was any single document called “kerygma” – the word simply refers to the material that was used in evangelism by various preachers in the early church.
The same applies to the term didache. There would have been a core of teaching that Paul used in establishing churches and training leaders. That material would have been generally the same in every church (i.e. qualifications for elders and deacons) but flexible enough to adapt to a slightly different cultural situation (the difference between the qualifications list in 1 Timothy and Titus, for example, show some adaptation for the situation on Crete where Titus was to appoint elders).
This core of teaching is found as early as Acts 2:42, where we are told that the new converts were devoted to the daily instruction of the apostles. Since all of these converts in the early part of Acts are Jews, and likely observant Jews in Acts 2, the need for ethical instruction would have been less of a priority than instruction in the teachings of Jesus (i.e. doctrine – Christology (who was Jesus, what did he teach) and Eschatology (the Christ is returning very soon). It is not unlikely that at this stage that the stories of Jesus’ acts and his teachings began to be passed from the Apostles to their disciples.
Some bibliography: E. G. Selwyn, The First Epistle of St. Peter, 363-466; Philip Carrington, The Primitive Christian Catechism; A. M. Hunter, Paul and his Predecessors; C. H. Dodd, The Apostolic Preaching and its Developments; Everett F. Harrison, “Some Patterns of the New Testament Didache” BSac V119 #474 (Apr 62) 118-129; V. P. Furnish, Theology and Ethics in Paul, 68-111.