Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Another coboundary operator for differential forms with values in the
  Lie algebra bundle of a group bundle   Kock [Bull. Austral. Math. Soc., 25 (1982), 357-386] has considered
differential forms with values in a group in a context where neighborhood
relations are available. By doing so, he has made it clear where the so-called
Maurer-Cartan formula should come from. In this paper, while we retain the
classical definition of differential form with values in the Lie algebra of a
group, we propose another definition of coboundary operator for the de Rham
complex in a highly general microlinear context, in which neighborhood
relations are no longer in view. Using this new definition of the coboundary
operator, it is to be shown that the main result of Kock's paper mentioned
above still prevails in our general microlinear context. Our considerations
will be carried out within the framework of groupoids.

1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat