让检测器同时识别新类别和新场景，且不需重新训练。

Open-domain open-vocabulary detection (ODOVD) requires detectors to generalize to both novel categories and unseen domains, making it more challenging than open-vocabulary detection. Existing methods typically train open-vocabulary detectors together with domain generalization modules from scratch, leading to high training cost. we propose ExDet, a lightweight category-domain collaborative generalization framework for ODOVD that enhances the cross-category and cross-domain generalization of existing detectors. ExDet consists of Text-Guided Extrapolation (TGE), a lightweight Detector-Compatible Rectification (DCR) module, and ExRPN. Specifically, TGE exploits the DeltaSpace property of vision-language models (VLMs) to infer category- and domain-aware proxy visual prototypes from text. DCR is learned from the TGE-generated prototypes in a detector training-free and real-data-free manner, and is inserted after the classification head at inference to rectify representations toward a detector-compatible source-domain visual distribution, thereby enhancing classification for targets from novel categories and unseen domains. ExRPN recalibrates proposal scores by combining semantic similarity with RPN confidence, improving recall for novel and domain-shifted objects while providing better support for subsequent classification and DCR. ExDet achieves SOTA performance on OD-LVIS, OV-LVIS, Objects365, and MSOSB.