In topology a dynamical system is given by a couple (X, f), where X is a topological space and f : X → X is a continuous map. Dimitrov — Haiden — Katzarkov — Kontsevich generalised this notion to that of a categorical dynamical system. To measure the complexity of such system, they also introduced the concept of categorical entropy. A famous theorem of Gromov and Yomdin relates the topological entropy of a holomorphic automorphism of a complex manifold with the action of the automorphism in cohomology. In this talk I will report on joint work with Jongmyeong Kim in which we provide a sufficient condition that ensures that (a weaker version of) an analogue theorem holds in categorical dynamics.