Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Autocompact objects of Ab5 categories   The aim of the paper is to describe autocompact objects in Ab5-categories,
i.e. objects in cocomplete abelian categories with exactness preserving
filtered colimits of exact sequences, whose covariant Hom-functor commutes with
copowers of the object itself. A characterization of non-autocompact object is
given, a general criterion of autocompactness of an object via the structure of
its endomorphism ring is presented and a criterion of autocompactness of
products is proven.

28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph