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Titlebook: Galois Connections and Applications; K. Denecke,M. Erné,S. L. Wismath Book 2004 Springer Science+Business Media Dordrecht 2004 Algebra.Ari

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Graham Cox,Philip Lowe,Michael Winterother algebraic, topological, order-theoretical, categorical and logical theories..We sketch the development of Galois connections, both in their covariant form (adjunctions) and in the contravariant form (polarities) through the last three centuries and illustrate their importance by many examples.
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https://doi.org/10.1007/978-981-19-0928-3tal algebras. On one side there are many different subsets of the set of first order formulas, which one wants to use as a concept of . in some special context, and where one is interested in the closure operators induced by restricting the . to this special subset. On the other hand the polarity in
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https://doi.org/10.1007/978-981-10-4325-3quires exactly that both . and t have complexity ≥ 1. We generalize this definition to any integer . ≥1 by saying that a non-trivial identity . is .-normal when both . and . have complexity ≥ .. A variety will be called .-normal when all its non-trivial identities are .-normal. Using results from th
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https://doi.org/10.1007/978-981-19-3555-8ne) and the category of relational systems of a given arity (where arities are considered to be ordinals). We show that objects of the obtained coreflective subcategory of the category of closure spaces are suitable for applications to digital topology because their connectedness is a certain type o
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