Recent successes in self-supervised learning (SSL) model spatial co-occurrences of visual features either by masking portions of an image or by aggressively cropping it. Here, we propose a new way to model spatial co-occurrences by aligning local representations (before pooling) with a global image representation. We present CO-SSL, a family of instance discrimination methods and show that it outperforms previous methods on several datasets, including ImageNet-1K where it achieves 71.5% of Top-1 accuracy with 100 pre-training epochs. CO-SSL is also more robust to noise corruption, internal corruption, small adversarial attacks, and large training crop sizes. Our analysis further indicates that CO-SSL learns highly redundant local representations, which offers an explanation for its robustness. Overall, our work suggests that aligning local and global representations may be a powerful principle of unsupervised category learning.