Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On perfectly generated weight structures and adjacent $t$-structures   This paper is dedicated to the study of smashing weight structures (one may
say that these are weight structures "coherent with arbitrary coproducts"), and
the application of their properties to $t$-structures. In particular, we prove
that hearts of compactly generated $t$-structures are Grothendieck abelian;
this statement strengthens earlier results of several other authors.
  The central theorem of the paper is as follows: any perfect set of objects of
a triangulated category generates a weight structure; we say that weight
structures obtained this way are perfectly generated. An important family of
perfectly generated weight structures are the ones adjacent to compactly
generated $t$-structures; they give injective cogenerators for the hearts of
the latter. We also establish the following not so explicit result: any
smashing weight structure on a well generated triangulated category (this class
of categories contains compactly generated ones) is perfectly generated;
actually, we prove more than that.
  Moreover, we give a classification of compactly generated torsion theories
(these generalize both weight structures and $t$-structures) that extends the
corresponding result of D. Pospisil D. and J. \v{S}\v{t}ovi\v{c}ek to arbitrary
smashing triangulated categories.

20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat