Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Almost Split Triangles and Morphisms Determined by Objects in
  Extriangulated Categories   Let $(\mathfrak{C},\mathbb{E},\mathfrak{s})$ be an Ext-finite, Krull-Schmidt
and $k$-linear extriangulated category with $k$ a commutative artinian ring. We
define an additive subcategory $\mathfrak{C}_r$ (respectively,
$\mathfrak{C}_l$) of $\mathfrak{C}$ in terms of the representable functors from
the stable category of $\mathfrak{C}$ modulo $\mathfrak{s}$-injectives
(respectively, $\mathfrak{s}$-projectives) to $k$-modules, which consists of
all $\mathfrak{s}$-projective (respectively, $\mathfrak{s}$-injective) objects
and objects isomorphic to direct summands of finite direct sums of all third
(respectively, first) terms of almost split $\mathfrak{s}$-triangles. We
investigate the subcategories $\mathfrak{C}_r$ and $\mathfrak{C}_l$ in terms of
morphisms determined by objects, and then give equivalent characterizations on
the existence of almost split $\mathfrak{s}$-triangles.

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The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
9
The categories of this paper are: nlin
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The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph