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https://hdl.handle.net/2440/84750
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DC Field | Value | Language |
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dc.contributor.author | Stevenson, D. | - |
dc.date.issued | 2012 | - |
dc.identifier.citation | Theory and Applications of Categories, 2012; 26(28):768-787 | - |
dc.identifier.issn | 1201-561X | - |
dc.identifier.uri | http://hdl.handle.net/2440/84750 | - |
dc.description.abstract | Given a bisimplicial set, there are two ways to extract from it a simplicial set: the diagonal simplicial set and the less well known total simplicial set of Artin and Mazur. There is a natural comparison map between these simplicial sets, and it is a theorem due to Cegarra and Remedios and independently Joyal and Tierney, that this comparison map is a weak homotopy equivalence for any bisimplicial set. In this paper we will give a new, elementary proof of this result. As an application, we will revisit Kan's simplicial loop group functor G. We will give a simple formula for this functor, which is based on a factorization, due to Duskin, of Eilenberg and Mac Lane’s classifying complex functor W. We will give a new, short, proof of Kan’s result that the unit map for the adjunction G ⊣ W is a weak homotopy equivalence for reduced simplicial sets. | - |
dc.description.statementofresponsibility | Danny Stevenson | - |
dc.language.iso | en | - |
dc.publisher | Mount Allison University | - |
dc.rights | © Danny Stevenson, 2012. | - |
dc.source.uri | http://www.tac.mta.ca/tac/volumes/26/28/26-28.pdf | - |
dc.title | Décalage and Kan's simplicial loop group functor | - |
dc.title.alternative | Decalage and Kan's simplicial loop group functor | - |
dc.type | Journal article | - |
pubs.publication-status | Published | - |
dc.identifier.orcid | Stevenson, D. [0000-0003-4399-7632] | - |
Appears in Collections: | Aurora harvest 2 Mathematical Sciences publications |
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