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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 Duality Theory for Clones Kerkhoff, Sebastian 12 October 2011 (has links) (PDF) In this thesis, we generalize clones (as well as their relational counterparts and the relationship between them) to categories. Based on this framework, we introduce a general duality theory for clones and apply it to obtain new results for clones on finite sets. Klon Dualitätstheorie Kategorientheorie Operation Relation Duale Operation Duale Relation Polymorphismus Invarianz Bewahren Klone über distributiven Verbänden Klone über Algebren Galois-Theorie clone duality theory category theory operation relation dual operation dual relation polymorphism invariance preserving clones over distributive lattices clones over algebras Galois theory ddc:510 rvk:SK 200 Universelle Algebra Dualitätstheorie Kategorientheorie
3	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
4	A General Duality Theory for Clones Kerkhoff, Sebastian 28 June 2011 (has links) In this thesis, we generalize clones (as well as their relational counterparts and the relationship between them) to categories. Based on this framework, we introduce a general duality theory for clones and apply it to obtain new results for clones on finite sets. info:eu-repo/classification/ddc/510 ddc:510

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