In the context of pose-invariant object recognition and retrieval, we demonstrate that it is possible to achieve significant improvements in performance if both the category-based and the object-identity-based embeddings are learned simultaneously during training. In hindsight, that sounds intuitive because learning about the categories is more fundamental than learning about the individual objects that correspond to those categories. However, to the best of what we know, no prior work in pose-invariant learning has demonstrated this effect. This paper presents an attention-based dual-encoder architecture with specially designed loss functions that optimize the inter- and intra-class distances simultaneously in two different embedding spaces, one for the category embeddings and the other for the object-level embeddings. The loss functions we have proposed are pose-invariant ranking losses that are designed to minimize the intra-class distances and maximize the inter-class distances in the dual representation spaces. We demonstrate the power of our approach with three challenging multi-view datasets, ModelNet-40, ObjectPI, and FG3D. With our dual approach, for single-view object recognition, we outperform the previous best by 20.0% on ModelNet40, 2.0% on ObjectPI, and 46.5% on FG3D. On the other hand, for single-view object retrieval, we outperform the previous best by 33.7% on ModelNet40, 18.8% on ObjectPI, and 56.9% on FG3D.