Propounding a general categorical framework for the extension of dualities, we present new proof de Vries Duality Theorem category KHaus compact Hausdorff spaces and their continuous maps, as an restricted Stone duality. Then, applying dualization to duality, give alternative duality Tych Tychonoff that was provided by Bezhanishvili, Morandi Olberding. In process doing so, obtain theorems both ...

We analyze the no-cloning theorem in quantum mechanics through the lens of the proposed ER=EPR (Einstein-Rosen = Einstein-Podolsky-Rosen) duality between entanglement and wormholes. In particular, we find that the no-cloning theorem is dual on the gravity side to the no-go theorem for topology change, violating the axioms of which allows for wormhole stabilization and causality violation. Such ...

We prove that the variety of nuclear implicative semilattices is locally finite, thus generalizing Diego’s Theorem. The key ingredients our proof include coloring technique and construction universal models from modal logic. For this we develop duality theory for finite semilattices, Köhler duality. main result remains true bounded give an alternative Theorem, provide explicit description free ...

We continue the investigation of H-Galois extensions of linear categories, where H is a Hopf algebra. In our main result, the Theorem 2.2, we characterize this class of extensions in the case when H is finite dimensional. As an application, we prove a version of the Duality Theorem for crossed products with invertible cocycle. Introduction The duality theorems for actions and coactions originat...

We extend our previous duality theorem for Markov processes by equipping the processes with a pseudometric and the algebras with a notion of metric diameter. We are able to show that the isomorphisms of our previous duality theorem become isometries in this quantitative setting. This opens the way to developing theories of approximate reasoning for probabilistic systems.

We give several related versions of global Grothendieck Duality for unbounded complexes on noetherian formal schemes. The proofs, based on a nontrivial adaptation of Deligne’s method for the special case of ordinary schemes, are reasonably self-contained, modulo the Special Adjoint Functor Theorem. An alternative approach, inspired by Neeman and based on recent results about “Brown Representabi...