Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homological systems and bocses   We show that, up to Morita equivalence, any finite-dimensional algebra with a
suitable homological system, admits an exact Borel subalgebra. This generalizes
a theorem by Koenig, K\"ulshammer and Ovsienko, which holds for
quasi-hereditary algebras. Our proof follows the same general scheme proposed
by these authors, in a more general context: we associate a differential graded
tensor algebra with relations, using the structure of $A_{\infty}-$algebra of a
suitable Yoneda algebra, and use its category of modules to describe the
category of filtered modules associated to the given homological system.

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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph