Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relative Torsion Classes, relative tilting and relative silting modules   Let $\Lambda$ be an Artin algebra. In 2014, T. Adachi, O. Iyama and I. Reiten
proved that the torsion funtorially finite classes in $\mathrm{mod}\,(\Lambda)$
can be described by the $\tau$-tilting theory. The aim of this paper is to
introduce the notion of $F$-torsion class in $\mathrm{mod}\,(\Lambda)$, where
$F$ is an additive subfunctor of $\mathrm{Ext}^1_\Lambda,$ and to characterize
when these clases are preenveloping and $F$-preenveloping. In order to do that,
we introduce the notion of $F$-presilting $\Lambda$-module. The latter is both
a generalization of $\tau$-rigid and $F$-tilting in $\mathrm{mod}(\Lambda).$

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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph