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In this paper, we study a new representation-learning task, which we termed as disassembling object representations. Given an image featuring multiple objects, the goal of disassembling is to acquire a latent representation, of which each part corresponds to one category of objects. Disassembling thus finds its application in a wide domain such as image editing and few- or zero-shot learning, as it enables category-specific modularity in the learned representations. To this end, we propose an unsupervised approach to achieving disassembling, named Unsupervised Disassembling Object Representation (UDOR). UDOR follows a double auto-encoder architecture, in which a fuzzy classification and an object-removing operation are imposed. The fuzzy classification constrains each part of the latent representation to encode features of up to one object category, while the object-removing, combined with a generative adversarial network, enforces the modularity of the representations and integrity of the reconstructed image. Furthermore, we devise two metrics to respectively measure the modularity of disassembled representations and the visual integrity of reconstructed images. Experimental results demonstrate that the proposed UDOR, despited unsupervised, achieves truly encouraging results on par with those of supervised methods.