Categorical entropy, (co-)t-structures and ST-triples

Abstract

In this paper, we study a dynamical property of an exact endofunctor Φ : D→ D of a triangulated category D . In particular, we are interested in the following question: Given full triangulated subcategories A, B⊂ D such that Φ (A) ⊂ A and Φ (B) ⊂ B , how the categorical entropies of Φ | A and Φ | B are related? To answer this question, we introduce new entropy-type invariants using bounded (co-)t-structures with finite (co-)hearts and prove their basic properties. We then apply these results to answer our question for the situation where A has a bounded t-structure and B has a bounded co-t-structure which are, in some sense, dual to each other. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.