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Crime prediction is crucial for public safety and resource optimization, yet is very challenging due to two aspects: i) the dynamics of criminal patterns across time and space, crime events are distributed unevenly on both spatial and temporal domains; ii) time-evolving dependencies between different types of crimes (e.g., Theft, Robbery, Assault, Damage) which reveal fine-grained semantics of crimes. To tackle these challenges, we propose Spatial-Temporal Sequential Hypergraph Network (ST-SHN) to collectively encode complex crime spatial-temporal patterns as well as the underlying category-wise crime semantic relationships. In specific, to handle spatial-temporal dynamics under the long-range and global context, we design a graph-structured message passing architecture with the integration of the hypergraph learning paradigm. To capture category-wise crime heterogeneous relations in a dynamic environment, we introduce a multi-channel routing mechanism to learn the time-evolving structural dependency across crime types. We conduct extensive experiments on two real-world datasets, showing that our proposed ST-SHN framework can significantly improve the prediction performance as compared to various state-of-the-art baselines. The source code is available at: https://github.com/akaxlh/ST-SHN.