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1. • CommentRowNumber1.
   • CommentAuthorStephenGaito
   • CommentTimeOct 30th 2009
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   Author: StephenGaito
   Format: MarkdownI have just posed the question: If we want to weaken this even further to provide a simplicial model of, for example, a ((?,2)-category?, how would we do this? Would we apply the lifting condition on all but three of the indicies… and if so which three? (The first, last and ????) at [quasi-category](http://ncatlab.org/nlab/show/quasi-category). Any and all thoughts would be appreciated.

   I have just posed the question:

    If we want to weaken this even further to provide a 
    simplicial model of, for example, a ((?,2)-category?, 
    how would we do this?
   
    Would we apply the lifting condition on all but three of 
    the indicies… and if so which three? (The first, last and ????)
   

   at quasi-category.

   Any and all thoughts would be appreciated.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeOct 31st 2009
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   Author: Urs
   Format: Markdownthere doesn't seem to be an obvious generalization of the step that takes one from the notion of Kan complexes to that of quasi-categories. Instead, the full notion of weak horn filler conditions for omega-categories seems to be [[Dominic Verity]]'s notion of [[complicial set]].

   there doesn't seem to be an obvious generalization of the step that takes one from the notion of Kan complexes to that of quasi-categories.

   Instead, the full notion of weak horn filler conditions for omega-categories seems to be Dominic Verity's notion of complicial set.