Various side information has been exploited in recommender systems to help users finding items they prefer to alleviate data sparsity. Because item category can be used to view the user's preference in a high-level scope and an item can have more than one associated category, the existing works leverage this characteristic, that enriches the information density of item, to further improve the recommendation performance. However, the existing works either treat item categories or their correlations as additional information to compute the similarity between users and items, or introduce category hierarchy as a latent factor into matrix factorization (MF) models. In these works, each item corresponds to a category set, that makes it too difficult to utilize item category's potential and valuable information. In this paper, we propose a novel combinatorial category space based recommendation model, which can fully exploit item category information and reduce the difficulty by converting the relationship between item and its categories from one-to-many to one-to-one. It considers a combinatorial category associated with an item, not each of them individually. Specifically, we first define a combinatorial category space (CCS), which is viewed as a subset-superset lattice of item categories. Then semantic relations and semantic distances are defined to model a user preference, and a compound graph (CoGraph) is constructed to model users' interactive behaviors in CCS, respectively. Finally, two recommendation models, CCSRank and CCSMF, are exploited on user interactive graph. We carry out extensive experimental evaluations on two real datasets to show the effectiveness of our model.