I gave the movie Inception another watch recently, and I found a lack of discussion on their types in forum searches. These are initial impressions I had of the characters, rather than a dogmatic statement of their types. It is worth noting that these characters are, in a sense, not so much characters as they are archetypes.
Dominic Cobb, the Extractor: SLE.
Arthur, the Point Man: LII.
Ariadne, the Architect: IEE (SEI?).
Eames, the Forger: EIE.
Saito, the Tourist: LSI.
Yusuf, the Chemist: SLI.
Fischer, the Mark: EII.
Mal Cobb, the Shade: IEI.