Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Lattice of Subobject Closed Subcategories and Colocal Type   We consider abelian length categories, a generalization of module categories
over Artin algebras. Let $\mathcal{A}$ be an abelian length category of colocal
type. We show that the lattice $\mathsf{S}(\mathcal{A})$ of full additive
subobject closed subcategories of $\mathcal{A}$ is distributive. Furthermore,
we give a characterization of abelian length categories of colocal type.
  If $A$ is an algebra of colocal type over an algebraically closed field, then
this characterization is especially simple and we can describe the lattice
$\mathsf{S(mod} ~A)$ up to isomorphism.

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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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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: eess
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The categories of this paper are: adap-org
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The categories of this paper are: cs