Urcohomologies and cohomologies of N-complexes

作者：Hiramatsu Naoya^*; Kato Goro C

来源：Portugaliae Mathematica, 2010, 67(4): 511-524.

DOI：10.4171/PM/1875

• N-complex
• N-exactness
• complexifying functor
• urcohomology

For a general sequence of objects and morphisms, we construct two N-complexes. Then we can define cohomologies (i, k)-type of the N-complexes not only on a diagonal region but also in the triangular region. We obtain an invariant defined on a general sequence of objects and morphisms. For a short exact sequence of N-complexes, we get the associated long exact sequence generalizing the classical long exact sequence. Lastly, several properties of the vanishing cohomologies of N-complexes are given.

• 出版日期2010