Who are the hypocrites associated with fasting in the Didache? The early Christian teaching Didache states that Christians should not fast like the hypocrites:


  Your fasts must not be identical with those of the hypocrites. They fast on Mondays and Thursdays; but you should fast on Wednesdays and Fridays. [Chapter 8]


Who are the hypocrites? A rival Christian group? The Pharisees? Someone else?
It is indeed about the Pharisees. Here's what Shmuel Safrai's paper “Religion in Everyday Life" says:


  Mondays and Thursdays, which were synagogue days, when country-folk came to town and the courts sat and the Torah was read, were the favoured days for public and private fasts. People would assemble for prayer, mention the reason for the fast, as follows from a baraita in the Babylonian Talmud. Most texts which mention fasting on Mondays and Thursdays are later than 70 C. E. though some are definitely earlier. Epiphanius says that these were the days of the Pharisees’ fasts in Jesus’ time, and the Didache warns against fasting ‘along with the hypocrites’ (the Pharisees) on these days, urging for Wednesday and Friday instead. The Pharisee in Luke who boasted of his twice-weekly fasting must have meant Mondays and Thursdays. But the custom was confined to certain circles among the Pharisees and their disciples. (page 816)