Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattices of theories   We show that there is a bijection between the subtoposes of the classifying
topos of a geometric theory T over a signature L and the closed geometric
theories over L which are `quotients' of the theory T; next, we analyze how
classical topos-theoretic constructions on the lattice of subtoposes of a given
topos can be transferred, via the bijection above, to logical constructions in
the corresponding lattice of theories.

5
The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
1
The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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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: q-fin
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The categories of this paper are: econ
14
The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: cond-mat