Abstract
The purpose of this chapter is to revisit, expand and simplify the “E 2-homotopy theory” of Dwyer-Kan-Stover [E 2], [HG] which built simplicial resolutions of pointed path connected topological spaces out of spheres. Using the notion of a spiral model category Q in (2.4) we prove the existence of the spiral homotopy category Ho(ΔQ)s of simplicial objects in Q in (3.5). This is the analogue of an E 2-homotopy theory. Simplicial resolutions of objects in Q live in the spiral homotopy category.
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© 1999 Springer-Verlag Berlin Heidelberg
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Baues, HJ. (1999). Resolutions in Model Categories. In: Combinatorial Foundation of Homology and Homotopy. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11338-7_4
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DOI: https://doi.org/10.1007/978-3-662-11338-7_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08447-8
Online ISBN: 978-3-662-11338-7
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