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In mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures in a one-to-one fashion.

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Aug 26, 2011 · This article compares three notions of duality that are relevant in these contexts: duality of convex bodies, duality of projective varieties, ...

Duality in the general course of human affairs seems to be a juxtaposition of comple- mentary or opposite concepts. This frequently leads to poetical ...

Nov 11, 2015 · The first goal of this paper is to provide an abstract framework in which to formulate and study local duality in various algebraic and topological contexts.

Jun 20, 2019 · In this paper we describe a self-dual context which allows one to establish the same theorems in the case of non-abelian group-like structures.

Jul 29, 2023 · In mathematics, one often has an equivalence of categories between algebra-like objects and space-like objects. Such an idea has many incarnations.

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In mathematics, coherent duality is any of a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex ...

Jul 11, 2023 · Instances of “dualities” relating two different, maybe opposing, but to some extent equivalent concepts or phenomena are ubiquitous in mathematics.

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An algebraic theory of dualities based on the notion of bond algebras is developed. This framework deals with classical and quantum dualities in a unified ...

Aug 17, 2011 · To get a duality with complete lattices, the second result characterizes those context morphisms that correspond to complete lattice ...