Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elementary equivalences and accessible functors   We introduce the notion of $\lambda$-equivalence and $\lambda$-embeddings of
objects in suitable categories. This notion specializes to
$L_{\infty\lambda}$-equivalence and $L_{\infty\lambda}$-elementary embedding
for categories of structures in a language of arity less than $\lambda$, and
interacts well with functors and $\lambda$-directed colimits. We recover and
extend results of Feferman and Eklof on "local functors" without fixing a
language in advance. This is convenient for formalizing Lefschetz's principle
in algebraic geometry, which was one of the main applications of the work of
Eklof.

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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: q-alg
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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: stat
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th