Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Model categories of quiver representations   Gillespie's Theorem gives a systematic way to construct model category
structures on $\mathscr{C}( \mathscr{M} )$, the category of chain complexes
over an abelian category $\mathscr{M}$.
  We can view $\mathscr{C}( \mathscr{M} )$ as the category of representations
of the quiver $\cdots \rightarrow 2 \rightarrow 1 \rightarrow 0 \rightarrow -1
\rightarrow -2 \rightarrow \cdots$ with the relations that two consecutive
arrows compose to $0$. This is a self-injective quiver with relations, and we
generalise Gillespie's Theorem to other such quivers with relations. There is a
large family of these, and following Iyama and Minamoto, their representations
can be viewed as generalised chain complexes.
  Our result gives a systematic way to construct model category structures on
many categories. This includes the category of $N$-periodic chain complexes,
the category of $N$-complexes where $\partial^N = 0$, and the category of
representations of the repetitive quiver $\mathbb{Z} A_n$ with mesh relations.

35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph