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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeFeb 21st 2011
• (edited Feb 21st 2011)

have created model structure on reduced simplicial sets

(I thought I had a vague memory that this or something similarly titled already existed, but apparently it didn’t).

Also added a little bit more detail on the Quillen equivalence with simplicial groups here and there, notably in the last section at groupoid object in an (infinity,1)-category

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeApr 13th 2012

the model structure on reduced simplicial sets: is is cofibrantly generated? Does the projective model structure on functors with values in it exist?

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeApr 13th 2012

Never mind, Danny kindly points out that it follows easily from prop. A.2.6.13 of HTT.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeFeb 28th 2017

I have added to model structure on reduced simplicial sets statement and (immediate) proof that reduced suspension/looping (co-)restricts to a Quillen endo-adjunction on reduced simplicial sets (here)

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeMar 1st 2017

Some questions:

Is the model structure on reduced simplicial sets still right proper?

And how about 2-reduced simplicial sets and $n$-reduced simplicial sets? Will they still carry the analogous model structures? And will they be right proper?