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Topological triangulated categories [PDF]
, 2012 In this paper we explain certain systematic differences between algebraic and topological triangulated categories. A triangulated category is algebraic if it admits a differential graded model, and topological if it admits a model in the form of a stable
Schwede, Stefan
core +2 more sources
Codescent theory II: cofibrant approximations [PDF]
Homology, Homotopy and Applications, 2006 28 ...
Balmer, Paul, Matthey, Michel
openaire +3 more sources
Lax monoidal adjunctions, two‐variable fibrations and the calculus of mates
Proceedings of the London Mathematical Society, Volume 127, Issue 4, Page 889-957, October 2023., 2023 Abstract We provide a calculus of mates for functors to the ∞$\infty$‐category of ∞$\infty$‐categories and extend Lurie's unstraightening equivalences to show that (op)lax natural transformations correspond to maps of (co)cartesian fibrations that do not necessarily preserve (co)cartesian edges. As a sample application, we obtain an equivalence between
Rune Haugseng +3 more
wiley +1 more source
On the motivic Segal conjecture
Journal of Topology, Volume 16, Issue 3, Page 1258-1313, September 2023., 2023 Abstract We establish motivic versions of the theorems of Lin and Gunawardena, thereby confirming the motivic Segal conjecture for the algebraic group μℓ$\mu _\ell$ of ℓ$\ell$th roots of unity, where ℓ$\ell$ is any prime. To achieve this we develop motivic Singer constructions associated to the symmetric group Sℓ$S_\ell$ and to μℓ$\mu _\ell$, and ...
Thomas Gregersen, John Rognes
wiley +1 more source
Homotopy of manifolds stabilized by projective spaces
Journal of Topology, Volume 16, Issue 3, Page 1237-1257, September 2023., 2023 Abstract We study the homotopy of the connected sum of a manifold with a projective space, viewed as a typical way to stabilize manifolds. In particular, we show a loop homotopy decomposition of a manifold after stabilization by a projective space, and provide concrete examples.
Ruizhi Huang, Stephen Theriault
wiley +1 more source
The univalence axiom for elegant Reedy presheaves [PDF]
, 2015 We show that Voevodsky's univalence axiom for intensional type theory is valid in categories of simplicial presheaves on elegant Reedy categories. In addition to diagrams on inverse categories, as considered in previous work of the author, this includes ...
Shulman, Michael
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Differential graded Koszul duality: An introductory survey
Bulletin of the London Mathematical Society, Volume 55, Issue 4, Page 1551-1640, August 2023., 2023 Abstract This is an overview on derived nonhomogeneous Koszul duality over a field, mostly based on the author's memoir L. Positselski, Memoirs of the American Math. Society 212 (2011), no. 996, vi+133. The paper is intended to serve as a pedagogical introduction and a summary of the covariant duality between DG‐algebras and curved DG‐coalgebras, as ...
Leonid Positselski
wiley +1 more source
A uniqueness theorem for stable homotopy theory [PDF]
, 1999 In this paper we study the global structure of the stable homotopy theory of spectra. We establish criteria for when the homotopy theory associated to a given stable model category agrees with the classical stable homotopy theory of spectra.
Schwede, Stefan, Shipley, Brooke
core +3 more sources
On an extension of the notion of Reedy category [PDF]
, 2008 We extend the classical notion of a Reedy category so as to allow non-trivial automorphisms. Our extension includes many important examples occuring in topology such as Segal's category Gamma, or the total category of a crossed simplicial group such as ...
Clemens Berger +3 more
core +6 more sources
On Relative Homotopy Groups of Modules
International Journal of Mathematics and Mathematical Sciences, 2007 In his book “Homotopy Theory and Duality,” Peter Hilton described the concepts of relative homotopy theory in module theory. We study in this paper the possibility of parallel concepts of fibration and cofibration in module theory, analogous to the ...
C. Joanna Su
doaj +1 more source