Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abelian subcategories of triangulated categories induced by simple
  minded systems   If $k$ is a field, $A$ a finite dimensional $k$-algebra, then the simple
$A$-modules form a simple minded collection in the derived category
$\operatorname{D}^b( \operatorname{mod} A )$. Their extension closure is
$\operatorname{mod} A$; in particular, it is abelian. This situation is
emulated by a general simple minded collection $\mathcal{S}$ in a suitable
triangulated category $\mathcal{C}$. In particular, the extension closure
$\langle \mathcal{S} \rangle$ is abelian, and there is a tilting theory for
such abelian subcategories of $\mathcal{C}$. These statements follow from
$\langle \mathcal{S} \rangle$ being the heart of a bounded $t$-structure.
  It is a defining characteristic of simple minded collections that their
negative self extensions vanish in every degree. Relaxing this to vanishing in
degrees $\{ -w+1, \ldots, -1 \}$ where $w$ is a positive integer leads to the
rich, parallel notion of $w$-simple minded systems, which have recently been
the subject of vigorous interest.
  If $\mathcal{S}$ is a $w$-simple minded system for some $w \geqslant 2$, then
$\langle \mathcal{S} \rangle$ is typically not the heart of a $t$-structure.
Nevertheless, using different methods, we will prove that $\langle \mathcal{S}
\rangle$ is abelian and that there is a tilting theory for such abelian
subcategories. Our theory is based on Quillen's notion of exact categories, in
particular a theorem by Dyer which provides exact subcategories of triangulated
categories.
  The theory of simple minded systems can be viewed as "negative cluster
tilting theory". In particular, the result that $\langle \mathcal{S} \rangle$
is an abelian subcategory is a negative counterpart to the result from (higher)
positive cluster tilting theory that if $\mathcal{T}$ is a cluster tilting
subcategory, then $( \mathcal{T} * \Sigma \mathcal{T} )/[ \mathcal{T} ]$ is an
abelian quotient category.

35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex