New tasks are often similar in structure to old ones. Animals that take advantage of such conserved or “abstract” task structures can master new tasks with minimal training. To understand the neural basis of this abstraction, we developed a novel behavioural paradigm for mice and recorded from their medial frontal neurons as they learned. Freely moving mice learned multiple tasks where they had to visit 4 rewarded locations in sequence (ABCD) on a 3x3 spatial maze. Tasks shared the same circular transition structure (… ABCDABCD …) but differed in the locations and geometric arrangement of rewards. As well as improving across tasks, mice inferred that A followed D (i.e. completed the loop) on the very first trial of a new task. This “zero-shot inference” is only possible if animals had learned the abstract structure of the task. Medial frontal cortex (mFC) neurons showed several signatures of internally organized tuning to abstract task-space. Firstly, the majority of state-tuned neurons in the mFC responded to the mouse’s “location” in abstract task space, conserving their state tuning across distinct tasks. Secondly, we found robust, task-stage modulated offline replay of activity in task-space during sleep. Thirdly, a minority of state-tuned neurons remapped across tasks. Preliminary evidence suggests that such remapping is quasi-coherent across neurons, consistent with the existence of task-space modules analogous to modules of grid-cells that coherently remap in physical space. These findings point to separable neuronal substrates for internally organised representations of task structure that may guide abstraction in the mammalian brain.