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• CommentRowNumber1.
• CommentAuthorKarol Szumiło
• CommentTimeOct 7th 2013
• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeOct 7th 2013

Thanks, nice!

• CommentRowNumber3.
• CommentAuthorMike Shulman
• CommentTimeOct 7th 2013

Does Prop. 2(2) mean that any elegant Reedy category has fibrant constants, or is there a missing hypothesis that $R$ itself has fibrant constants?

• CommentRowNumber4.
• CommentAuthorKarol Szumiło
• CommentTimeOct 8th 2013

No assumption is missing and hence all elegant Reedy categories have fibrant constants.

In fact, while I was writing this entry I realized that I can’t think of any example of a non-elegant Reedy category with fibrant constants. This makes me wonder whether these notions coincide. It would be quite interesting since fibrant constants seem like a lot weaker condition than elegance.