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Intro; Preface; Contents; Part I Quantum Reality; A Generalisation of Stone Duality to Orthomodular Lattices; 1 Introduction; 2 Background and Preliminary Results; 2.1 Ortholattices and Orthomodular Lattices; 2.2 Distributive Substructure of an Orthomodular Lattice; 2.3 Stone Duality; 2.4 Complete Orthomodular Lattices and Their Boolean Substructure; 2.5 Stonean Spaces and Stone Duality for Complete Boolean Algebras; 2.6 Galois Connections and the Adjoint Functor Theorem for Posets; 3 The Spectral Presheaf of an Orthomodular Lattice; 3.1 Definition; 3.2 Maps Between Spectral Presheaves
3.3 The Category of mathcalD-Valued Presheaves3.4 The Category of mathcalC-Valued Copresheaves; 3.5 Dual Equivalences and Stone Duality; 3.6 Concrete Isomorphisms Between Spectral Presheaves and Bohrifications; 3.7 The Spectral Presheaf of an OML Is a Complete Invariant; 3.8 Interpretation of the Results so Far; 3.9 The Spectral Presheaf of a Complete OML Is a Complete Invariant; 4 Representing a Complete Orthomodular Lattice; 4.1 Clopen Subobjects of the Spectral Presheaf; 4.2 The Clopen Subobjects Form a Complete Bi-Heyting Algebra; 4.3 Daseinisation as Representation of a Complete OML
4.4 Some Physical Interpretation4.5 The Adjoint of Daseinisation; 4.6 Regaining a cOML from the Algebra of Clopen Subobjects; 5 Conclusion; References; Bell's Local Causality is a d-Separation Criterion; 1 Introduction; 2 Bayesian Networks and d-Separation; 3 Bell's Local Causality in a Local Physical Theory; 4 Shielder-Off Regions are d-Separating; 5 Conclusions; References; Local Operations and Completely Positive Maps in Algebraic Quantum Field Theory; 1 Introduction; 2 Algebraic Quantum Field Theory; 3 Completely Positive Maps; 4 Relatively Local Operations; 5 Conclusion; References
Symmetries in Exact Bohrification1 Bohrification; 2 Symmetries in Quantum Theory on Hilbert Space; 3 Symmetries in Algebraic Quantum Theory; 4 Hamhalter's Theorem; 5 Projections; References; Categorial Local Quantum Physics; 1 The Main Idea of the Categorial Paradigm for Quantum Field Theory; 2 The Covariant Functor of Categorial Local Quantum Physics; 3 Causal Locality Conditions on the Covariant Functor; 3.1 The BASIC Axioms: Einstein Locality and Time Slice; 3.2 Amending the Basic Axioms by Adding Morphism Co-possibility as Subsystem Independence
3.3 Amending the Basic Axioms by Adding the Categorial Split Property3.4 The Tensor Axiom; 4 Relation of Axiom Systems; References; Part II Quantum Information; Reverse Data-Processing Theorems and Computational Second Laws; 1 Introduction; 2 A Reverse-Data Processing Theorem for Classical Channels; 2.1 Comparison of Noisy Channels; 2.2 Replacing H with Hmin; 3 The Fundamental Lemma for Quantum Channels; 3.1 Quantum Statistical Morphisms; 4 A Semiclassical (Semiquantum) Reverse-Data Processing Theorem; 5 A Fully Quantum Reverse Data-Processing Theorem
3.3 The Category of mathcalD-Valued Presheaves3.4 The Category of mathcalC-Valued Copresheaves; 3.5 Dual Equivalences and Stone Duality; 3.6 Concrete Isomorphisms Between Spectral Presheaves and Bohrifications; 3.7 The Spectral Presheaf of an OML Is a Complete Invariant; 3.8 Interpretation of the Results so Far; 3.9 The Spectral Presheaf of a Complete OML Is a Complete Invariant; 4 Representing a Complete Orthomodular Lattice; 4.1 Clopen Subobjects of the Spectral Presheaf; 4.2 The Clopen Subobjects Form a Complete Bi-Heyting Algebra; 4.3 Daseinisation as Representation of a Complete OML
4.4 Some Physical Interpretation4.5 The Adjoint of Daseinisation; 4.6 Regaining a cOML from the Algebra of Clopen Subobjects; 5 Conclusion; References; Bell's Local Causality is a d-Separation Criterion; 1 Introduction; 2 Bayesian Networks and d-Separation; 3 Bell's Local Causality in a Local Physical Theory; 4 Shielder-Off Regions are d-Separating; 5 Conclusions; References; Local Operations and Completely Positive Maps in Algebraic Quantum Field Theory; 1 Introduction; 2 Algebraic Quantum Field Theory; 3 Completely Positive Maps; 4 Relatively Local Operations; 5 Conclusion; References
Symmetries in Exact Bohrification1 Bohrification; 2 Symmetries in Quantum Theory on Hilbert Space; 3 Symmetries in Algebraic Quantum Theory; 4 Hamhalter's Theorem; 5 Projections; References; Categorial Local Quantum Physics; 1 The Main Idea of the Categorial Paradigm for Quantum Field Theory; 2 The Covariant Functor of Categorial Local Quantum Physics; 3 Causal Locality Conditions on the Covariant Functor; 3.1 The BASIC Axioms: Einstein Locality and Time Slice; 3.2 Amending the Basic Axioms by Adding Morphism Co-possibility as Subsystem Independence
3.3 Amending the Basic Axioms by Adding the Categorial Split Property3.4 The Tensor Axiom; 4 Relation of Axiom Systems; References; Part II Quantum Information; Reverse Data-Processing Theorems and Computational Second Laws; 1 Introduction; 2 A Reverse-Data Processing Theorem for Classical Channels; 2.1 Comparison of Noisy Channels; 2.2 Replacing H with Hmin; 3 The Fundamental Lemma for Quantum Channels; 3.1 Quantum Statistical Morphisms; 4 A Semiclassical (Semiquantum) Reverse-Data Processing Theorem; 5 A Fully Quantum Reverse Data-Processing Theorem