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Although self-/un-supervised methods have led to rapid progress in visual representation learning, these methods generally treat objects and scenes using the same lens. In this paper, we focus on learning representations for objects and scenes that preserve the structure among them. Motivated by the observation that visually similar objects are close in the representation space, we argue that the scenes and objects should instead follow a hierarchical structure based on their compositionality. To exploit such a structure, we propose a contrastive learning framework where a Euclidean loss is used to learn object representations and a hyperbolic loss is used to encourage representations of scenes to lie close to representations of their constituent objects in a hyperbolic space. This novel hyperbolic objective encourages the scene-object hypernymy among the representations by optimizing the magnitude of their norms. We show that when pretraining on the COCO and OpenImages datasets, the hyperbolic loss improves downstream performance of several baselines across multiple datasets and tasks, including image classification, object detection, and semantic segmentation. We also show that the properties of the learned representations allow us to solve various vision tasks that involve the interaction between scenes and objects in a zero-shot fashion. Our code can be found at \url{https://github.com/shlokk/HCL/tree/main/HCL}.