Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cofree compositions of coalgebras   We develop the notion of the composition of two coalgebras, which arises
naturally in higher category theory and in the theory of species. We prove that
the composition of two cofree coalgebras is again cofree, and we give
sufficient conditions that ensure the composition is a one-sided Hopf algebra.
We show these conditions are satisfied when one coalgebra is a graded Hopf
operad D and the other is a connected graded coalgebra with coalgebra map to D.
We conclude by computing the primitive elements for compositions of coalgebras
built on the vertices of multiplihedra, composihedra, and hypercubes.

17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
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
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics