Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relational Operations in FOLE   This paper discusses relational operations in the first-order logical
environment {FOLE}. Here we demonstrate how FOLE expresses the relational
operations of database theory in a clear and implementable representation. An
analysis of the representation of database tables/relations in FOLE reveals a
principled way to express the relational operations. This representation is
expressed in terms of a distinction between basic components versus composite
relational operations. The 9 basic components fall into three categories:
reflection (2), Booleans or basic operations (3), and adjoint flow (4). Adjoint
flow is given for signatures (2) and for type domains (2), which are then
combined into full adjoint flow. The basic components are used to express
various composite operations, where we illustrate each of these with a
flowchart. Implementation of the composite operations is then expressed in an
input/output table containing four parts: constraint, construction, input, and
output. We explain how limits and colimits are constructed from diagrams of
tables, and then classify composite relational operations into three
categories: limit-like, colimit-like and unorthodox.

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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: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: math
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an