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We give a general method of constructing positive stable model structures for symmetric spectra over an abstract simplicial symmetric monoidal model category. The method is based on systematic localization, in Hirschhorns sense, of a ceratin positive projective model structure on spectra, where positivity basically means the truncation of the zero slice. The localization above is by the set of stabilizing morphisms, or their truncated version.
We show how to construct a Gamma-bicategory from a symmetric monoidal bicategory, and use that to show that the classifying space is an infinite loop space upon group completion. We also show a way to relate this construction to the classic Gamma-cat
We show that a derivator is stable if and only if homotopy finite limits and homotopy finite colimits commute, if and only if homotopy finite limit functors have right adjoints, and if and only if homotopy finite colimit functors have left adjoints.
We present a family of model structures on the category of multicomplexes. There is a cofibrantly generated model structure in which the weak equivalences are the morphisms inducing an isomorphism at a fixed stage of an associated spectral sequence.
We initiate the study of model structures on (categories induced by) lattice posets, a subject we dub homotopical combinatorics. In the case of a finite total order $[n]$, we enumerate all model structures, exhibiting a rich combinatorial structure e
In this paper, we provide a new proof of the stable Adams conjecture. Our proof constructs a canonical null-homotopy of the stable J-homomorphism composed with a virtual Adams operation, by applying the $mathrm{K}$-theory functor to a multi-natural t