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

In this paper, we study a dynamical property of an exact endofunctor $Φ: \mathcal{D} \to \mathcal{D}$ of a triangulated category $\mathcal{D}$. In particular, we are interested in the following question: Given full triangulated subcategories $\mathcal{A},\mathcal{B} \subset \mathcal{D}$ such that $Φ(\mathcal{A}) \subset \mathcal{A}$ and $Φ(\mathcal{B}) \subset \mathcal{B}$, how the categorical entropies of $Φ|_\mathcal{A}$ and $Φ|_\mathcal{B}$ 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 $\mathcal{A}$ has a bounded t-structure and $\mathcal{B}$ has a bounded co-t-structure which are, in some sense, dual to each other.

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