Stable homotopy of algebraic theories

By S. Schwede. 2001

61 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/31a541df5c2f8e7c5c5a645e9624131ed3f4e6e9

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In Algebra and Number Theory

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Citations in the corpus

Homotopy completion and topological Quillen homology of structured ring spectra (2011, background): “An important first step in establishing these theorems was provided by the characterization given by Schwede [68] of flat stable cofibrations in ModR in terms of objects with an R0-action; see Proposition 7.34 below for the needed generalization of this.”
Stable model categories are categories of modules (2003, background): “Another motivation for this paper and an early instance of Theorem 3.1.1 came from the stabilization of the model category of algebras over an algebraic theory [54].”
A uniqueness theorem for stable homotopy theory (2000, unknown): “It is shown in [ Sch1 , Lemma A.3] that the stable brations of spectra are precisely the maps with the RLP with respect to the set J lv[J st.”
Homotopical algebraic geometry. I. Topos theory. (2002, methodology): “By a result of McClure, Schw ¨anzl and Vogt (see [EKMM, IX, Th. 3.3]), S1 ⊗L B is isomorphic to THHA(B; B) ≡ THH(B|A) in Ho(AlgA) and is”
Every homotopy theory of simplicial algebras admits a proper model (2000, methodology): “ibe a model category structure on the category of simplicial algebras over any I-sorted theory Tbased on simplicial sets. The model category structure we construct coincides with those constructed in [Sch] and [Bad00]. 7.1. Closed model category structure. Let Tbe an I-sorted theory over sS. Recall ”
Homology and cohomology of E∞ ring spectra (2004, background): “…in CB/B. Basterra [1, §3] constructs an “indecomposables” functor Q from NB to MB that is left adjoint to the “zero multiplication” functor Z from MB to NB. Precisely, the indecomposables functor QN is defined as the (point-set) pushout QN = ∗ ∪(N∧BN) N in the category of B-modules of the…”
Generalized Brown representability in homotopy categories (2005, unknown): “(iii) The model category Sp of spectra with the stable Bousfield-Friedlander model category structure (see [5]) is ω-combinatorial (see [40] A.”