On Some Relationships Between Spectral Sequences And The New Exact Sequences

Abstract

     In this paper I introduce and study relationships between spectral

sequences and the new exact sequences . I will show that the  new exact  sequence is the second derived exact couple .

       Let

be an exact couple ,  we derive  to get the second exact couple    which is the new exact sequence  . the process of derivation can

 be iterated indefinitely, yielding an infinite sequence of exact couples .

      I establish some results ,for examples ; 

      The class of all exact couples and morphisms between these couples formed a category . There is a functor from the category of   into   .

     If   

 .

       If    be any   , then

 , and    .