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https://hdl.handle.net/2440/84750
Type: | Journal article |
Title: | Décalage and Kan's simplicial loop group functor |
Other Titles: | Decalage and Kan's simplicial loop group functor |
Author: | Stevenson, D. |
Citation: | Theory and Applications of Categories, 2012; 26(28):768-787 |
Publisher: | Mount Allison University |
Issue Date: | 2012 |
ISSN: | 1201-561X |
Statement of Responsibility: | Danny Stevenson |
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. |
Rights: | © Danny Stevenson, 2012. |
Published version: | http://www.tac.mta.ca/tac/volumes/26/28/26-28.pdf |
Appears in Collections: | Aurora harvest 2 Mathematical Sciences publications |
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