Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: DB Category: Denotational Semantics for View-based Database Mappings   We present a categorical denotational semantics for a database mapping, based
on views, in the most general framework of a database integration/exchange.
Developed database category DB, for databases (objects) and view-based mappings
(morphisms) between them, is different from Set category: the morphisms (based
on a set of complex query computations) are not functions, while the objects
are database instances (sets of relations). The logic based schema mappings
between databases, usually written in a highly expressive logical language (ex.
LAV, GAV, GLAV mappings, or tuple generating dependency) may be functorially
translated into this "computation" category DB. A new approach is adopted,
based on the behavioral point of view for databases, and behavioral
equivalences for databases and their mappings are established. By introduction
of view-based observations for databases, which are computations without
side-effects, we define a fundamental (Universal algebra) monad with a
power-view endofunctor T. The resulting 2-category DB is symmetric, so that any
mapping can be represented as an object (database instance) as well, where a
higher-level mapping between mappings is a 2-cell morphism. Database category
DB has the following properties: it is equal to its dual, complete and
cocomplete. Special attention is devoted to practical examples: a query
definition, a query rewriting in GAV Database-integration environment, and the
fixpoint solution of a canonical data integration model.

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The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: stat