What is the relationship between recognizing objects and drawing objects? We examine the possibility that both functions are supported by a common internal representation. First, we show that a model of ventral visual cortex only optimized to recognize objects in photographs generalizes to drawings of objects, suggesting that the capacity for visual abstraction is rooted in the functional architecture of the visual system. Next, we tested whether practice drawing objects might alter how those and other objects are represented. On each trial, participants sketched an object. The model then guessed the identity of the sketched object, providing real-time feedback. We found that repeatedly sketched objects were better recognized after training, while sketches of unpracticed but similar objects worsened. These results show that visual production can reshape the representational space for objects: by differentiating trained objects and merging other nearby objects in the space.