Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Projective covers of flat contramodules   We show that a direct limit of projective contramodules (over a right linear
topological ring) is projective if it has a projective cover. A similar result
is obtained for $\infty$-strictly flat contramodules of projective dimension
not exceeding $1$, using an argument based on the notion of the topological
Jacobson radical. Covers and precovers of direct limits of more general classes
of objects, both in abelian categories with exact and with nonexact direct
limits, are also discussed, with an eye towards the Enochs conjecture about
covers and direct limits, using locally split (mono)morphisms as the main
technique. In particular, we offer a simple elementary proof of the Enochs
conjecture for the left class of an $n$-tilting cotorsion pair in an abelian
category with exact direct limits.

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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
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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: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con