* symmetric simplicial sets
@ 2006-03-13 14:17 Jiri Rosicky
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From: Jiri Rosicky @ 2006-03-13 14:17 UTC (permalink / raw)
To: categories
One advantage of symmetric simplicial sets is that their model
category structure is determined, cf. (*), by taking cofibrations
as monomorphisms. It means that the classical homotopy category
Ho (of CW-complexes) can be obtained just from the category S
of symmetric simplicial sets (without any additional data).
Simplicial sets do not have this property (it was also observed
by J. H. Smith). In (*), we have used this property of S to give
an elementary proof of an important result of D. Dugger saying
that Ho is a free homotopy theory over a point.
(*) J. Rosicky and W. Tholen, Left-determined model categories
and universal homotopy theories, TAMS 355 (2003), 3611-3623.
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