Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free limits of free algebras   Consider a diagram $\cdots \to F_3 \to F_2\to F_1$ of algebraic systems,
where $F_n$ denotes the free object on $n$ generators and the connecting maps
send the extra generator to some distinguished trivial element. We prove that
(a) if the $F_i$ are free associative algebras over a fixed field then the
limit in the category of graded algebras is again free on a set of homogeneous
generators; (b) on the other hand, the limit in the category of associative
(ungraded) algebras is a free formal power series algebra on a set of
homogeneous elements, and (c) if the $F_i$ are free Lie algebras then the limit
in the category of graded Lie algebras is again free.

17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph