Re: What is a "principal fibration" ?

I do not remember the notion in Grothendieck's work, but the term princial fibration was extensively used with simplicial sets. the theory is very pretty and can be found in the survey by Curtis in Adv. in Maths. 6 (1971) 107 - 209. Given the close connections between Simplicial sets and category theory this may provide a solution to your problem. Tim Porter mas013@uk.ac.bangor