论文标题
分类熵，（共同）T结构和St-Triples
Categorical entropy, (co-)t-structures and ST-triples
论文作者
论文摘要
在本文中，我们研究了一个精确的endofunctor $φ的动态属性：\ Mathcal {d} \ to \ Mathcal {d} $的三角形类别$ \ MATHCAL {D} $。特别是，我们对以下问题感兴趣：给定完整的三角形子类别$ \ MATHCAL {a}，\ MATHCAL {B} \ subset \ Mathcal \ Mathcal \ Mathcal {d} $，使得$φ（\ Mathcal {a}） \ Mathcal {B} $，$φ| _ \ Mathcal {a} $和$φ| _ \ Mathcal {B} $的分类熵如何相关？为了回答这个问题，我们使用有限（共同）心脏的有界（共同）T结构引入了新的熵型不变性，并证明了它们的基本属性。然后，我们将这些结果应用于回答我们的问题，以解决$ \ Mathcal {a} $具有有界的T结构，而$ \ Mathcal {B} $具有有界的Co-T结构，从某种意义上来说，彼此双重。
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.
