You won't find this type of CB that will fit in any of the typical home style load center breaker panels, as they simply don't make them.
The intent here is device level protection, secondary to your main breaker panel. 15 amp breaker in your main panel feeding the branch circuit your compressor is on. This CB goes between your main breaker and the motor.
As I tried, but failed to explain before, is your compressor, as well as mine are appliance devices. Original intent was to be used inside of an appliance, like maybe a vending machine or some other gizmo... Who really knows the initial intent. But, inside of that gizmo, you most likely would have device level protection on the compressor, as well as other devices in the assembly.
Me thinks I should not have brought this subject up.