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Jan 24, 2010 at 12:51 comment added Tim Porter My intuition comes from extending the join in simplicial complexes which is described in a classical source such as Spanier. The examples that Phil Ehlers looked at in his thesis again made a lot of sense and showed how the augmentation aspect comes in. (I can send you a link to Phil's work but first have a look at Joins for (augmented) simplicial sets, Jour. Pure Applied Algebra, 145 (2000) 37-44 to see if that helps.
Jan 24, 2010 at 10:39 comment added Harry Gindi I mean, I've mostly resolved the problem, but I still don't really have an intuitive feeling for the join of arbitrary simplicial sets.
Jan 24, 2010 at 10:32 history answered Tim Porter CC BY-SA 2.5