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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.

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Showing 1 to 2 of 2 (0.015 seconds)
1

A General Galois Theory for Operations and Relations in Arbitrary Categories

Kerkhoff, Sebastian 20 September 2011 (has links) (PDF)
In this paper, we generalize the notions of polymorphisms and invariant relations to arbitrary categories. This leads us to a Galois connection that coincides with the classical case from universal algebra if the underlying category is the category of sets, but remains applicable no matter how the category is changed. In analogy to the situation in universal algebra, we characterize the Galois closed classes by local closures of clones of operations and local closures of what we will introduce as clones of (generalized) relations. Since the approach is built on purely category-theoretic properties, we will also discuss the dualization of our notions.
Klon
Operation
Relation
Invarianz
Polymorphismen
bewahren
Kompabilität
Galois Verbindung
Galois Theory
Co-Klon
Co-Relation
Dualität
Kategorientheorie
clone
operation
relation
invariance
polymorphism
preserving
compability
Galois connection
Galois theory
coclone
corelation
duality theory
category theory
ddc:510
rvk:SK 200
rvk:SK 320
Galois-Verbindung
Universelle Algebra
Kategorientheorie
2

A General Galois Theory for Operations and Relations in Arbitrary Categories

Kerkhoff, Sebastian 20 September 2011 (has links)
In this paper, we generalize the notions of polymorphisms and invariant relations to arbitrary categories. This leads us to a Galois connection that coincides with the classical case from universal algebra if the underlying category is the category of sets, but remains applicable no matter how the category is changed. In analogy to the situation in universal algebra, we characterize the Galois closed classes by local closures of clones of operations and local closures of what we will introduce as clones of (generalized) relations. Since the approach is built on purely category-theoretic properties, we will also discuss the dualization of our notions.
info:eu-repo/classification/ddc/510
ddc:510

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