Why H Z-algebra Spectra are Differential Graded Algebras?

In homological algebra, to understand commutative rings R, one studies R-modules, chain complexes of R-modules and their monoids, the differential graded R-algebras. The category of R-modules has a rich structure, but too rigid to efficiently work with homological invariants and homotopy invariant properties. It appears more appropriate to operate in the derived category D(R), which is the homotopy category of differential graded R-modules. Algebra of symmetric spectra offers a generalization of homological algebra. In this frame, spectra are objects that take the place of abelian groups; in particular, the analogue of the initial ring Z is the sphere spectrum S. Tensoring over S endows the category of spectra with a symmetric monoidal smash product, analogous to the tensor product of abelian groups. Thus, spectra are S-modules, and ring spectra, which extend the notion of rings, are the S-algebras. To any discrete ring R, one can associate the Eilenberg-Mac Lane ring spectrum HR, which is commutative if R is

Left-induced model structures and diagram categories

We prove existence results a la Jeff Smith for left-induced model category structures, of which the injective model structure on a diagram category is an important example. We further develop the notions of fibrant generation and Postnikov presentation from Hess, which are dual to a weak form of cofibrant generation and cellular presentation. As examples, for k a field and H a differential graded Hopf algebra over k, we produce a left-induced model structure on augmented H-comodule algebras and show that the category of bounded below chain complexes of finite-dimensional k-vector spaces has a Postnikov presentation. To conclude, we investigate the fibrant generation of (generalized) Reedy categories. In passing, we also consider cofibrant generation, cellular presentation, and the small object argument for Reedy diagrams.Comment: 33 pages; v2 fixes an error in the construction of the Postnikov presentation in section 3 and contains several minor improvements suggested by the referee. To appear in the Proceedings of the August 2013 "Women in Topology" workshop at BIRS, which will be published by Contemporary Mathematic

ВЛИЯНИЕ ФАКТОРА НЕСТАБИЛЬНОСТИ ВНЕШНЕЙ СРЕДЫ НА СТРАТЕГИЮ ВЗАИМОДЕЙСТВИЯ ГОСУДАРСТВА И БИЗНЕСА В ВЫСОКОТЕХНОЛОГИЧНЫХ СФЕРАХ РОССИЙСКОЙ ЭКОНОМИКИ

The types of the unstable state of the macroeconomic environment affecting the strategy of forming government and business. Applied to high-tech industries studied forms of public-private partnerships. The structure of the organizational problems that arise in the creation and development of effective public-private partnership whose solution minimizes the negative effects of environmental factors.Рассмотрены виды нестабильного состояния макроэкономической среды, влияющие на формирование стратегии развития государства и бизнеса. Применительно к высокотехнологичным отраслям экономики исследованыформыгосударственно-частногопартнерства. Предложенаструктураорганизационныхзадач, возникающихвсфересозданияи эффективногоразвитиягосударственно-частногопартнерства, решение которыхминимизируетдействиенегативныхфактороввнешнейсред