Aspect-based sentiment analysis (ABSA) have been extensively studied, but little light has been shed on the quadruple extraction consisting of four fundamental elements: aspects, categories, opinions and sentiments, especially with implicit aspects and opinions. In this paper, we propose a new method iACOS for extracting Implicit Aspects with Categories and Opinions with Sentiments. First, iACOS appends two implicit tokens at the end of a text to capture the context-aware representation of all tokens including implicit aspects and opinions. Second, iACOS develops a sequence labeling model over the context-aware token representation to co-extract explicit and implicit aspects and opinions. Third, iACOS devises a multi-label classifier with a specialized multi-head attention for discovering aspect-opinion pairs and predicting their categories and sentiments simultaneously. Fourth, iACOS leverages informative and adaptive negative examples to jointly train the multi-label classifier and the other two classifiers on categories and sentiments by multi-task learning. Finally, the experimental results show that iACOS significantly outperforms other quadruple extraction baselines according to the F1 score on two public benchmark datasets.