Honeywell Control Circuit Board 51306515-175 CC-TAIN11 Digital Input Module
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Honeywell Control Circuit Board 51306515-175 CC-TAIN11 Digital Input Module
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SIMILAR PRODUCTS CC-PAIH01 HLAI - HART CC-GAIX11 GI/IS Analog Input, Redundant X
Abstract. Let S be the sphere spectrum. We construct an
associative, commutative, and unital smash product in a complete
and cocomplete category MS of “S-modules” whose derived category DS
is equivalent to the classical stable homotopy category. This
allows a simple and algebraically manageable definition of
“S-algebras” and “commutative S-algebras” in terms of associative,
or associative and commutative, products R ∧S R −→ R. These notions
are essentially equivalent to the earlier notions of A∞ and E∞ ring
spectra, and the older notions feed naturally into the new
framework to provide plentiful examples. There is an equally simple
definition of R-modules in terms of maps R ∧S M −→ M. When R is
commutative, the category MR of R-modules also has an associative,
commutative, and unital smash product, and its derived category DR
has properties just like the stable homotopy category. Working in the derived category DR, we construct spectral sequences
that specialize to give generalized universal coefficient and
K¨unneth spectral sequences. Classical torsion products and Ext
groups are obtained by specializing our constructions to
Eilenberg-Mac Lane spectra and passing to homotopy groups, and the
derived category of a discrete ring R is equivalent to the derived
category of its associated Eilenberg-Mac Lane S-algebra. We also
develop a homotopical theory of R-ring spectra in DR, analogous to
the classical theory of ring spectra in the stable homotopy
category, and we use it to give new constructions as MU-ring
spectra of a host of fundamentally important spectra whose earlier
constructions were both more difficult and less precise. Contact person: Anna E-mail: wisdomlongkeji@163.com Cellphone: +0086-13534205279 |
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