Geometry & Topology
- Geom. Topol.
- Volume 18, Number 1 (2014), 103-140.
Commutative ring objects in pro-categories and generalized Moore spectra
We develop a rigidity criterion to show that in simplicial model categories with a compatible symmetric monoidal structure, operad structures can be automatically lifted along certain maps. This is applied to obtain an unpublished result of M J Hopkins that certain towers of generalized Moore spectra, closely related to the –local sphere, are –algebras in the category of pro-spectra. In addition, we show that Adams resolutions automatically satisfy the above rigidity criterion. In order to carry this out we develop the concept of an operadic model category, whose objects have homotopically tractable endomorphism operads.
Geom. Topol., Volume 18, Number 1 (2014), 103-140.
Received: 22 August 2012
Revised: 7 April 2013
Accepted: 13 June 2013
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.) 55U35: Abstract and axiomatic homotopy theory
Secondary: 18D20: Enriched categories (over closed or monoidal categories) 18D50: Operads [See also 55P48] 18G55: Homotopical algebra
Davis, Daniel G; Lawson, Tyler. Commutative ring objects in pro-categories and generalized Moore spectra. Geom. Topol. 18 (2014), no. 1, 103--140. doi:10.2140/gt.2014.18.103. https://projecteuclid.org/euclid.gt/1513732720