The behaviour of the \(\overline{W}\)-construction on the homotopy theory of bisimplicial sets. (English) Zbl 1145.55018
The aim of the paper is to compare the codiagonal functor and the diagonal functor from simplicial sets to bisimplicial sets which tranfer the ordinary model category of a simplicial set to a Quillen closed model structure and the Moerdijk closed model structure on the corresponding bisimplicial set, respectively. The authors prove several interesting relationships between these two closed model structures.
Reviewer: Goutam Mukherjee (Kolkata)
MSC:
| 55U10 | Simplicial sets and complexes in algebraic topology |
| 55U35 | Abstract and axiomatic homotopy theory in algebraic topology |
| 18G55 | Nonabelian homotopical algebra (MSC2010) |
| 18G30 | Simplicial sets; simplicial objects in a category (MSC2010) |
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