Abstract
The codiagonal functor \(\overline{W}\) transfers a Quillen closed model structure on the bisimplicial set category from the ordinary model category of simplicial sets. This bisimplicial model structure is different from the so called Moerdijk model structure, which is similarly transferred from simplicial sets but through the diagonal functor. We show the mutual relationship of these two closed model structures on the category of bisimplicial sets.
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The authors are much indebted to the referee, whose useful observations greatly improved our exposition.
The authors acknowledge support from the Ministerio de Eduación y Ciencia de España (Projects: MTM2004-01060, MTM2006-06317), FEDER, Consejería de Innovación de la Junta de Andalucía (Project: P06-FQM-1889) and project ‘Ingenio Mathematica (i-MATH)’ No. CSD2006-00032 (Consolider Ingenio 2010).
The second author thanks the University of Granada for its support and hospitality.
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Cegarra, A.M., Remedios, J. The behaviour of the \(\overline{W}\) -construction on the homotopy theory of bisimplicial sets. manuscripta math. 124, 427–457 (2007). https://doi.org/10.1007/s00229-007-0118-y
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DOI: https://doi.org/10.1007/s00229-007-0118-y