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This chapter uses categorical techniques to describe relations between various sets of operators on a Hilbert space, such as self-adjoint, positive, density, effect and projection operators.
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Effect algebras and unsharp quantum logics
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Semantics of weakening and contraction
B. Jacobs · 1994
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Examples, problems, and results in effect algebras
S. Gudder · 1996
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Representation theorem for convex effect algebras
S. Pulmannová and S. Gudder · 1998
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Semirings and their Applications
J. S. Golan · 1999
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Categorical Logic and Type Theory
B. Jacobs · 1999
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New Trends in Quantum Structures
A. Dvurečenskij and S. Pulmannová · 2000
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Quantum states and generalized observables: a simple proof of Gleason’s Theorem
P. Busch · 2003
The monad of probability measures over compact ordered spaces and its Eilenberg-Moore algebras
K. Keimel · 2008
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A categorical semantics of quantum protocols
S. Abramsky and B. Coecke · 2009
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Bar categories and star operations
E.J. Beggs and S. Majid · 2009
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Convexity, duality, and effects
B. Jacobs · 2010
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Exemplaric expressivity of modal logics
B. Jacobs and A. Sokolova · 2010
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New Structures in Physics
B. Coecke, editor · 2011
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On involutive monoidal categories
J.M. Egger · 2011
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