Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three variations on the linear independence of grouplikes in a coalgebra   The grouplike elements of a coalgebra over a field are known to be linearly
independent over said field. Here we prove three variants of this result. One
is a generalization to coalgebras over a commutative ring (in which case the
linear independence has to be replaced by a weaker statement). Another is a
stronger statement that holds (un-der stronger assumptions) in a commutative
bialgebra. The last variant is a linear independence result for characters (as
opposed to grouplike elements) of a bialgebra.

12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph