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HONEYWELL CC-GAOX11 REDUNDANT ANALOG OUTPUTGI / IS IOTA Red (16) Control Circuit Board
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| Yasakawa Motor, Driver SG- | Mitsubishi Motor HC-,HA- |
| Westinghouse Modules 1C-,5X- | Emerson VE-,KJ- |
| Honeywell TC-,TK- | GE Modules IC - |
| Fanuc motor A0- | Yokogawa transmitter EJA- |
SIMILAR PRODUCTS
51402089-100 EPDG2 EPDG2 Interface Card
51402447-100 EPDGC-1 EPDGC-1 I/O
51402447-200 EPDGC-2 EPDGC-2 I/O
51403135-100 Touch Screen Assy 21" Z
51403157-200 AUX PWR SUPPLY ASSY
51403158-100 Brightness/Contrast Buttn
51403165-400 Keyboard Tray Assembly Z
51108899-100 LCNFL LCNFL Paddle Board
51109701-100 MP-DFDTM2 MP-DFDTM2 Floppy Disk Dr
51109818-100 U.S. Media Pwr Supply
51109919-100 Clock Source Board
51195156-100 20Meg Bernoulli
51195156-200 Beta 20A Bernoulli
51195156-300 20ZA Meg Bernoulli Drive
51196483-100 150 MB Bernoulli Drive
51196929-135 Zip Drive 3.5 Internal Zip Drive
51303642-300 US Annuciator - Z Style
51304270-100 EPDG I/O EPDG I/O
51304584-100 EPDGP I/O EPDGP I/O Board
51304584-200 EPDGP EPDGP I/O Card
The last thirty years have seen the importation of more and more algebraic techniques into stable homotopy theory. Throughout this period, most work in stable homotopy theory has taken place in Boardman’s stable homotopy category [6], or in Adams’ variant of it [2], or, more recently, in Lewis and May’s variant [37]. That category is analogous to the derived category obtained from the category of chain complexes over a commutative ring k by inverting the quasi-isomorphisms. The sphere spectrum S plays the role of k, the smash product ∧ plays the role of the tensor product, and weak equivalences play the role of quasi-isomorphisms. A fundamental difference between the two situations is that the smash product on the underlying category of spectra is not associative and commutative, whereas the tensor product between chain complexes of k-modules is associative and commutative. For this reason, topologists generally work with rings and modules in the stable homotopy category, with their products and actions defined only up to homotopy. In contrast, of course, algebraists generally work with differential graded k-algebras that have associative point-set level multiplications.
We here introduce a new approach to stable homotopy theory that allows one to do point-set level algebra. We construct a new category MS of S-modules that has an associative, commutative, and unital smash product ∧S. Its derived category DS is obtained by inverting the weak equivalences; DS is equivalent to the classical stable homotopy category, and the equivalence preserves smash products. This allows us to rethink all of stable homotopy theory: all previous work in the subject might as well have been done in DS. Working on the point-set level, in MS, we define an S-algebra to be an S-module R with an associative and unital product R ∧S R −→ R; if the product is also commutative, we call R a commutative S-algebra. Although the definitions are now very simple, these are not new notions: they are refinements of the A∞ and E∞ ring spectra that were introduced over twenty years ago by May, Quinn, and Ray [47]. In general, the 1 2 INTRODUCTION latter need not satisfy the precise unital property that is enjoyed by our new Salgebras, but it is a simple matter to construct a weakly equivalent S-algebra from an A∞ ring spectrum and a weakly equivalent commutative S-algebra from an E∞ ring spectrum.
It is tempting to refer to (commutative) S-algebras as (commutative) ring spectra. However, this would introduce confusion since the term “ring spectrum” has had a definite meaning for thirty years as a stable homotopy category level notion. Ring spectra in the classical homotopical sense are not rendered obsolete by our theory since there are many examples that admit no S-algebra structure. In any case, the term S-algebra more accurately describes our new concept. With our theory, and the new possibilities that it opens up, it becomes vitally important to keep track of when one is working on the point-set level and when one is working up to homotopy. In the absence (or ignorance) of a good point-set level category of spectra, topologists have tended to be sloppy about this. The dichotomy will run through our work. The terms “ring spectrum” and “module spectrum” will always refer to the classical homotopical notions. The terms “S-algebra” and “S-module” will always refer to the strict point-set level notions.