How do human brains represent tasks of varying structure? The lateral prefrontal cortex (lPFC) flexibly represents task information. However, principles that shape lPFC representational geometry remain unsettled. We use deep sampling fMRI and pattern analyses to reveal the detailed structure of lPFC representational geometries as humans perform two distinct categorization tasks- one with flat, conjunctive categories and another with hierarchical, context-dependent categories. We show that lPFC encodes task-relevant information with task-tailored geometries of intermediate dimensionality. These geometries preferentially enhance the separability of task-relevant variables while encoding a subset in abstract form. Specifically, in the flat task, a global axis encodes response-relevant categories abstractly, while category-specific local geometries are high-dimensional. In the hierarchy task, a global axis abstractly encodes the higher-level context, while low-dimensional, context-specific local geometries compress irrelevant information and abstractly encode the relevant information. Comparing these task geometries exposes generalizable principles by which lPFC tailors representations to different tasks.