Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homologically optimal categories of sequences lead to N-complexes   We study the category of $\mathbb{Z}$-indexed sequences over an abelian
category and certain generalized homology functors for this category of
sequences which are indexed by positive integers $a$ and $b$. By looking at the
corresponding derived category, we show that there is an "optimal" subcategory
of sequences for every choice of our generalized homology functors, namely, the
category of $N$-complexes (sequences for which the differential $d$ satisfies
$d^N = 0$) where $N = a + b$. In this optimal case we show that our homology
functors reduce to Kapranov's homology functors $\operatorname{ker} d^a /
\operatorname{im} d^b$.

22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg