Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The cobordism category and Waldhausen's K-theory   This paper examines the category C^k_{d,n} whose morphisms are d-dimensional
smooth manifolds that are properly embedded in the product of a k-dimensional
cube with an (d+n-k)-dimensional Euclidean space. There are k directions to
compose k-dimensional cubes, so C^k_{d,n} is a (strict) k-tuple category. The
geometric realization of the k-dimensional multi-nerve is the classifying space
BC^k_{d,n}.
  At the end of the paper we construct an infinite loop map to Waldhausens
K-theory. \Omega BC^1_{d,n}-> A(BO(d)), We believe that the map factors through
\Omega^\infty\Sigma^\infty(BO(d)_+) and that the composite B{Diff}(M^d)\to
A(BO(d)) is homotopic to the map considered by Dwyer, Williams and Weiss.

15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio