Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic Kasparov K-theory. I   This paper is to construct unstable, Morita stable and stable bivariant
algebraic Kasparov $K$-theory spectra of $k$-algebras. These are shown to be
homotopy invariant, excisive in each variable $K$-theories. We prove that the
spectra represent universal unstable, Morita stable and stable bivariant
homology theories respectively.

34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn