When AI training data is legally called into question, copyright law is regularly the focus. Where personal data is involved, data protection law is also an obvious concern. Less prominent in the discussion so far, however, is the "Digital Markets Act" (DMA). This legal act, according to Art. 1(1) is intended to ensure "contestable and fair markets in the digital sector". As a risk to these objectives, the DMA identifies online platforms and, after a gatekeeper-designation, imposes certain obligations and prohibitions. As part of the GSLES Graduate School lecture series at the University of Würzburg, Tabea Bauermeister examined whether the DMA prohibits — or should prohibit — AI training with gatekeeper data.