Foundations, Sets and Categories
In this subdiscipline:
1,842 papers
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This paper defines and proves the correctness of the appropriate string diagrams for various kinds of monoidal categories with duals.
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It is common practice in both theoretical computer science and theoretical physics to describe the (static) logic of a system by means of a complete lattice. When formalizing the dynamics of such a system, the updates of that system organize…
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We expose the information flow capabilities of pure bipartite entanglement as a theorem - which embodies the exact statement on the `seemingly acausal flow of information' in protocols such as teleportation. We use this theorem to re-design and…
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Set Theory has experienced a rapid development in recent years, with major advances in forcing, inner models, large cardinals and descriptive set theory. The present book covers each of these areas, giving the reader an understanding of the ideas…
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We study quantum information and computation from a novel point of view. Our approach is based on recasting the standard axiomatic presentation of quantum mechanics, due to von Neumann, at a more abstract level, of compact closed categories with…
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In this work we use a notion of rank first introduced by James Baumgartner and Peter Dordal and later developed independently by the third author to show that adding a Hechler real has strong combinatorial consequences. We prove: 1) assuming omega1…
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This is the first paper in a series where we generalize the Categorical Quantum Mechanics program (due to Abramsky, Coecke, et al) to braided systems. In our view a uniform description of quantum information for braided systems has not yet emerged.…
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The placenta is essential for sustaining the growth of the fetus during gestation, and defects in its function result in fetal growth restriction or, if more severe, fetal death. Several molecular pathways have been identified that are essential for…
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The Open Colouring Axiom implies that the measure algebra cannot be embedded into P(N)/fin. We also discuss the errors in previous results on the embeddability of the measure algebra.
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In this chapter we survey some particular topics in category theory in a somewhat unconventional manner. Our main focus will be on monoidal categories, mostly symmetric ones, for which we propose a physical interpretation. These are particularly…
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Student (Bachelor)Bern, Switzerland -
Researcher (at a non-Academic Institution)Bellevue, Washington, United States -
Ph.D. StudentLisbon, Portugal -
Student (Master)Granada, Spain -
Other ProfessionalSantiago, Chile