• Corpus ID: 238253266

Substructural fixed-point theorems and the diagonal argument: theme and variations

@article{Roberts2021SubstructuralFT,
  title={Substructural fixed-point theorems and the diagonal argument: theme and variations},
  author={David Michael Roberts},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.00239}
}
Little could Cantor have foreseen exactly how far the principle of his simple proof in [Can92] would be extended. The technique of diagonalisation has appeared in many places, and this was captured by an abstract category-theoretic proof of a diagonal argument by Lawvere [Law06], applying to not just bare sets and functions, but more structured objects. A key ingredient of Cantor’s original proof2— 2 it is perhaps telling that Cantor didn’t originally run the diagonal argument on a list of real… 
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References

SHOWING 1-10 OF 54 REFERENCES
Diagonal arguments and cartesian closed categories
In May 1967 I had suggested in my Chicago lectures certain applications of category theory to smooth geometry and dynamics, reviving a direct approach to function spaces and therefore to functionals.
No-Cloning In Categorical Quantum Mechanics
Recently, the author and Bob Coecke have introduced a categorical formulation of Quantum Mechanics. In the present paper, we shall use it to open up a novel perspective on No-Cloning. What we shall
Modalities In Substructural Logics
This paper generalises Girard's results which embed intuitionistic logic into linear logic by showing how arbitrary substructural logics can be embedded into weaker substructural logics, using a
Brouwer's fixed-point theorem in real-cohesive homotopy type theory
  • Michael Shulman
  • Mathematics, Computer Science
    Mathematical Structures in Computer Science
  • 2017
We combine homotopy type theory with axiomatic cohesion, expressing the latter internally with a version of ‘adjoint logic’ in which the discretization and codiscretization modalities are
Physics, Topology, Logic and Computation: A Rosetta Stone
In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology.
Coherent Diagrammatic Reasoning in Compositional Distributional Semantics
TLDR
A graphical language for the (categorical formulation of) the nonassociative Lambek calculus is developed and it is shown the language is coherent with monoidal closed categories without associativity, in the style of Selinger’s survey paper.
Internal Universes in Models of Homotopy Type Theory
TLDR
This work shows how to construct a universe that classifies the Cohen-Coquand-Huber-Mortberg (CCHM) notion of fibration from their cubical sets model, starting from the assumption that the interval is tiny - a property that the intervals in cubical set does indeed have.
From Lawvere to Brandenburger-Keisler: Interactive forms of diagonalization and self-reference
TLDR
The Brandenburger–Keisler paradox in epistemic game theory is analyzed, which is a ‘two-person version of Russell's paradox’, and a general coalgebraic approach to the construction of assumption-complete models is outlined.
Semantics of lambda-I and of other substructure lambda calculi
  • B. Jacobs
  • Mathematics, Computer Science
    TLCA
  • 1993
TLDR
The ordinary untyped λ-calculus (the main object of study in [3]) will be denoted here by λK, which can be understood as the λI-Calculus without weakening: one cannot throw away variables.
An Introduction to Substructural Logics
TLDR
This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural' and systematically survey the new results and the significant impact that this class oflogics has had on a wide range of fields.
...
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2
3
4
5
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