Are you using an USB audio interface or are you using sound card/onboard audio?
Are you recording in 2 track mode or multi-track mode? In either mode you can select which input to use.
In any case to use a mono mic with a stereo input you should have it routed to the left channel as it defaults to mono sound if nothing is connected to the right channel. In Audition you can specify the channel to use for input and whether it is mono or stereo recording.