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# A cohomology operation of type

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In , the **cohomology operation** concept became central to , particularly , from the 1950s onwards, in the shape of the simple definition that if is a defining a , then a cohomology operation should be a from to itself. Throughout there have been two basic points:

In the the aspect is implicit in the use of , the of Hom-functors; if there is a bicommutant aspect, taken over the Steenrod algebra acting, it is only at a level. The convergence is to groups in , about which information is hard to come by. This connection established the deep interest of the cohomology operations for , and has been a research topic ever since. An has its own cohomology operations, and these may exhibit a richer set on constraints.

In the the aspect is implicit in the use of , the of Hom-functors; if there is a bicommutant aspect, taken over the Steenrod algebra acting, it is only at a level. The convergence is to groups in , about which information is hard to come by. This connection established the deep interest of the cohomology operations for , and has been a research topic ever since. An has its own cohomology operations, and these may exhibit a richer set on constraints.

Cohomology of CW complexes is by an , so by the a cohomology operation of type is given by a class of maps . Using once again, the cohomology operation is given by an element of .