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Categorical sensory representations are critical for many behaviors, including speech perception. In the auditory system, categorical information is thought to arise hierarchically, becoming increasingly prominent in higher-order cortical regions. The neural mechanisms that support this robust and flexible computation remain poorly understood. Here, we studied sound representations in the ferret primary and non-primary auditory cortex while animals engaged in a challenging sound discrimination task. Population-level decoding of simultaneously recorded single neurons revealed that task engagement caused categorical sound representations to emerge in non-primary auditory cortex. In primary auditory cortex, task engagement caused a general enhancement of sound decoding that was not specific to task-relevant categories. These findings are consistent with mixed selectivity models of neural disentanglement, in which early sensory regions build an overcomplete representation of the world and allow neurons in downstream brain regions to flexibly and selectively read out behaviorally relevant, categorical information.