Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Duality pairs, phantom maps, and definability in triangulated categories   We define duality triples and duality pairs in compactly generated
triangulated categories and investigate their properties. This enables us to
give an elementary way to determine whether a class is closed under pure
subobjects, pure quotients and pure extensions, as well as providing a way to
show the existence of approximations. One key ingredient is a new
characterisation of phantom maps. We pay particular attention to symmetric
(co)product closed duality pairs, which are shown to be nothing other than
(dual) definable categories. Localisations of duality pairs are considered,
alongside many examples that naturally arise in representation theory and
homotopy theory. It is shown that duality pairs abound; for example every class
of objects is shown to generate a duality pair.

30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int