Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniqueness of exact Borel subalgebras and bocses   Together with Koenig and Ovsienko, the first author showed that every
quasi-hereditary algebra can be obtained as the (left or right) dual of a
directed bocs. In this monograph, we prove that if one additionally assumes
that the bocs is basic, a notion we define, then this bocs is unique up to
isomorphism. This should be seen as a generalisation of the statement that the
basic algebra of an arbitrary associative algebra is unique up to isomorphism.
The proof associates to a given presentation of the bocs an
$A_\infty$-structure on the $\operatorname{Ext}$-algebra of the standard
modules of the corresponding quasi-hereditary algebra. Uniqueness then follows
from an application of Kadeishvili's theorem.

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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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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: stat
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex