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Sequential recommendation is the task of predicting the next items for users based on their interaction history. Modeling the dependence of the next action on the past actions accurately is crucial to this problem. Moreover, sequential recommendation often faces serious sparsity of item-to-item transitions in a user's action sequence, which limits the practical utility of such solutions. To tackle these challenges, we propose a Category-aware Collaborative Sequential Recommender. Our preliminary statistical tests demonstrate that the in-category item-to-item transitions are often much stronger indicators of the next items than the general item-to-item transitions observed in the original sequence. Our method makes use of item category in two ways. First, the recommender utilizes item category to organize a user's own actions to enhance dependency modeling based on her own past actions. It utilizes self-attention to capture in-category transition patterns, and determines which of the in-category transition patterns to consider based on the categories of recent actions. Second, the recommender utilizes the item category to retrieve users with similar in-category preferences to enhance collaborative learning across users, and thus conquer sparsity. It utilizes attention to incorporate in-category transition patterns from the retrieved users for the target user. Extensive experiments on two large datasets prove the effectiveness of our solution against an extensive list of state-of-the-art sequential recommendation models.