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Topos Models for Physics and Topos Theory [PDF]
Journal of Mathematical Physics, 2013 What is the role of topos theory in the topos models for quantum theory as used by Isham, Butterfield, Doring, Heunen, Landsman, Spitters and others? In other words, what is the interplay between physical motivation for the models and the mathematical framework used in these models?
Sander Wolters
arxiv +9 more sources
Axioms for Modelling Cubical Type Theory in a Topos [PDF]
Logical Methods in Computer Science, 2018 The homotopical approach to intensional type theory views proofs of equality as paths. We explore what is required of an object $I$ in a topos to give such a path-based model of type theory in which paths are just functions with domain $I$.
Ian Orton, Andrew M. Pitts
doaj +9 more sources
A category theory perspective on the Language of Thought: LoT is universal [PDF]
Frontiers in PsychologyThe Language of Thought (LoT) hypothesis proposes that some collections of mental states and processes are symbol systems to explain language-like systematic properties of thought.
Steven Phillips
doaj +2 more sources
Topos Quantum Theory with Short Posets [PDF]
Order, 2020 14 ...
John Harding, Chris Heunen
openalex +7 more sources
, 2006 735 pages. An updated and expanded version of the earlier submission math.CT/0306109 2/10/07: Various minor additions and corrections; added some material on combinatorial model categories to the appendix. 3/8/7: Actually uploaded the update this time; added material on fiber products of higher topoi.
Jacob Lurie
openalex +4 more sources
Topos Theory and ‘Neo-Realist’ Quantum Theory [PDF]
, 2009 Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasising the logical aspects. Each topos serves as a `mathematical universe' with an internal logic, which is used to assign truth-values to all propositions ...
Andreas Döring
openalex +5 more sources
Shared Protentions in Multi-Agent Active Inference [PDF]
EntropyIn this paper, we unite concepts from Husserlian phenomenology, the active inference framework in theoretical biology, and category theory in mathematics to develop a comprehensive framework for understanding social action premised on shared goals.
Mahault Albarracin +5 more
doaj +2 more sources
Intuitionist type theory and the free topos
Journal of Pure and Applied Algebra, 1980 In this article we study free toposes with the help of intuitionist type theory. Our treatment is self-contained and aims to be accessible to both categorists and logicians. We attempt to explain the relevant logic to the former and the categorical applications to the latter.
J. Lambek, Philip Scott
openalex +3 more sources
Review of the Topos Approach to Quantum Theory [PDF]
Canadian Journal of Physics, 2011 Topos theory has been suggested by Döring and Isham as an alternative mathematical structure with which to formulate, in general, physical theories. However, the motivation for using it to express quantum theory, lies in the desire to solve certain interpretational problems inherent in the standard formulation of the theory.
Cecilia Flori
openalex +5 more sources
First steps in synthetic guarded domain theory: step-indexing in the topos of trees [PDF]
Logical Methods in Computer Science, 2012 We present the topos S of trees as a model of guarded recursion. We study the internal dependently-typed higher-order logic of S and show that S models two modal operators, on predicates and types, which serve as guards in recursive definitions of terms,
Lars Birkedal +3 more
doaj +2 more sources