| Cohomology Operation |
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| CATEGORIES ABOUT COHOMOLOGY OPERATION | |
| algebraic topology | |
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#the operations can be studied by combinatorial means; and #the effect of the operations is to yield an interesting Bicommutant theory. The origin of these studies was the work of Norman Steenrod , who first defined the Steenrod Square operation for Singular Cohomology , in the case of mod 2 coefficients. The combinatorial aspect there arises as a formulation of the failure of a Natural Diagonal map, at Cochain level. The general theory of the Steenrod Algebra of operations has been brought into close relation with that of the Symmetric Group . In the Adams Spectral Sequence the ''bicommutant'' aspect is implicit in the use of Ext Functor s, the Derived Functor s of Hom-functors; if there is a bicommutant aspect, taken over the Steenrod algebra acting, it is only at a ''derived'' level. The convergence is to groups in Stable Homotopy Theory , about which information is hard to come by. This connection established the deep interest of the cohomology operations for Homotopy Theory , and has been a research topic ever since. An Extraordinary Cohomology Theory has its own cohomology operations, and these may exhibit a richer set on constraints. FORMAL DEFINITION A cohomology operation of type : is a Natural Transformation of functors : defined on CW Complex es. |
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