Results 11 to 20 of about 3,365 (87)
Correspondences and stable homotopy theory
Transactions of the London Mathematical Society, Volume 10, Issue 1, Page 124-155, December 2023., 2023 Abstract A general method of producing correspondences and spectral categories out of symmetric ring objects in general categories is given. As an application, stable homotopy theory of spectra SH$SH$ is recovered from modules over a commutative symmetric ring spectrum defined in terms of framed correspondences over an algebraically closed field ...
Grigory Garkusha
wiley +1 more source
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
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Axiomatic homotopy theory for operads [PDF]
, 2002 We give sufficient conditions for the existence of a model structure on operads in an arbitrary symmetric monoidal model category. General invariance properties for homotopy algebras over operads are deduced.Comment: 29 pages, revised for ...
Berger, Clemens, Moerdijk, Ieke
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Takayasu cofibrations revisited
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 2015 This note gives a new construction of Takayasu's cofibrations.
Nguyen, Dang Ho Hai, Ndhh +1 more
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Fibrations That are Cofibrations [PDF]
Proceedings of the American Mathematical Society, 1983 We give necessary and sufficient conditions for a homotopy cartesian square to be homotopy cocartesian. Specializing, we obtain a necessary and sufficient condition for a fibration to be a cofibration. We apply the above to localization of spaces and to acyclic maps.
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Fibrations That are Cofibrations. II [PDF]
Proceedings of the American Mathematical Society, 1989 We show that fibrations that are cofibrations can be described quite explicitly (in terms of localization) when the total space of the fibration is nilpotent and that, in the absence of nilpotency, no such simple characterization exists.
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Equivariant cofibrations and nilpotency [PDF]
Transactions of the American Mathematical Society, 1981 Let f : B → Y f:B \to Y be a cofibration whose cofiber is a Moore space. We give necessary and sufficient conditions for f f to be induced by a map of the desuspension of the cofiber into B B . These conditions are especially simple if B B and
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Homotopy (Pre-)Derivators of Cofibration Categories and Quasi-Categories
, 2018 We prove that the homotopy prederivator of a cofibration category is equivalent to the homotopy prederivator of its associated quasi-category of frames, as introduced by Szumi\l{}o.
Lenz, Tobias
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Assembly of constructible factorization algebras
Journal of Topology, Volume 19, Issue 1, March 2026.Abstract We provide a toolbox of extension, gluing, and assembly techniques for factorization algebras. Using these tools, we fill various gaps in the literature on factorization algebras on stratified manifolds, the main one being that constructible factorization algebras form a sheaf of symmetric monoidal ∞$\infty$‐categories.
Eilind Karlsson +2 more
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The localization sequence for the algebraic K-theory of topological K-theory
, 2006 We prove a conjecture of Rognes by establishing a localization cofiber sequence of spectra, K(Z) to K(ku) to K(KU) to Sigma K(Z), for the algebraic K-theory of topological K-theory. We deduce the existence of this sequence as a consequence of a devissage
Andrew J. Blumberg +4 more
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