Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cosilting complexes and AIR-cotilting modules   We introduce and study the new concepts of cosilting complexes, cosilting
modules and AIR-cotilting modules. We prove that the three concepts
AIR-cotilting modules, cosilting modules and quasi-cotilting modules coincide
with each other, in contrast with the dual fact that AIR-tilting modules,
silting modules and quasi-tilting modules are different. Further, we show that
there are bijections between the following four classes (1) equivalent classes
of AIR-cotilting (resp., cosilting, quasi-cotilting) modules, (2) equivalent
classes of 2-term cosilting complexes, (3) torsion-free cover classes and (4)
torsion-free special precover classes. We also extend a classical result of
Auslander and Reiten on the correspondence between certain contravariantly
finite subcategories and cotilting modules to the case of cosilting complexes.

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The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph