Which Adobe product?
In general, for non-Cloud perpetually licensed products: no, they're platform specific: Mac only or Windows only.
For Cloud, version then yes. You have up to 2 activations per license: Win/Win, Mac/Mac or Win/Mac.
Lightroom is the primary exception: both Cloud and non-Cloud are dual platform: Win and/or Mac.
What John said. Only CCM and specific products are cross-platform, all others platfor-specific based on the serial.
I'm specifically looking at Lightroom. Looks like I will be able to run both platforms... Now to figure out a goo file managment system if I'm editing photos on both systems.
I travel with a PC laptop (can't afford a MAC yet) so I will do some editing on the road for posts to facebook etc. and the heavy editing on the IMAC when we get back from holiday.
Thanks for your help.