Accessible Categories: The Foundations of Categorical Model Theory

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In this highly significant paper, I outline the implications of the critical methodology used in Demonstrations of Degree Absolutism: Zero-and-Four-Quarters Ontologies and objectively-coherent category theory in general predominately in In this highly significant paper, I outline the implications of the critical methodology used in Demonstrations of Degree Absolutism: Zero-and-Four-Quarters Ontologies and objectively-coherent category theory in general predominately in the work of Nathan Coppedge. Non-classical Markov logic and network analysis.

First order languages express properties of entities and their relationships in rich models of heterogeneous network phenomena. Markov logic is a set of techniques for estimating the probabilities of truth values of such properties.

This article generalizes Markov logic in order to allow nonclassical sets of truth values. The new methods directly support uncertainties in both data sources and values. The concepts and methods of categorical logic give precise guidelines for selecting sets of truth values based on the form of a network model.

Applications to alias detection, cargo shipping, insurgency analysis, and other problems are given. Open problems include complexity analysis and parallelization of algorithms. Metaphysical Typologies Part I. A sense of typologies for the first eight dimensions. Categorical sets describing n- dimensional universes coherently, ostensibly. I only go up to eight, because eight is the ideal number for confronting all major contradictions I only go up to eight, because eight is the ideal number for confronting all major contradictions contained within a category, e.

What everyone has been waiting for who studies my work intensely. It has been hard to locate until now How to Build a Dimensional Universe.

Categorical Foundations and Foundations of Category Theory

Follow up on my earlier paper on dimensional universes. Lists abbreviated properties of the first typological dimensions of metaphysics, and perhaps ambitious physics. Analysis of two interpretations of reason and the method, with importance for daily life.

Realizability of Homotopy Type Theory. This paper shows constructive alternatives for a couple of theorems that make simplicial sets a model of homotopy type theory. The constructive theories are valid in the exact completion of the category of assemblies. Ultimately this Ultimately this shows that simplicial PERs are a model of homotopy type theory. Nick Benton. Valeria de Paiva.


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A detailed sketch of a computer program which 'solves a lot of problems'. It would be great if someone would implement this.

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Propositional Calculus of Non-Causal Inference. I'm adopting Wikipedia's definition of 'mathematical logic', and applying it to my own work. In the genre of dimensional philosophy. Topological and category-theoretic aspects of abstract elementary classes. Classification theory for accessible categories. Related Topics.

Forking independence from the categorical point of view

Category Theory. Follow Following. So far, I love the notion that they both provide an underlying framework for most fields in pure maths. However, I have googled but there are not much resources out there about open questions of the application of CT and MT. Secondly, my lecturers are encouraging me to do CT and MT with applications in mind. Both at a masters thesis level and a doctorates? The interplay between CT and MT is pretty well established. The term to search for is locally accessible categories. Another subject to look at may be topos theory, again with plenty of material online.

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A complete, or even a very partial list of applications of CT and MT will require a lot of bytes. MT has applications in algebra and in analysis, and that alone is quite a lot. CT as a language is useful pretty much throughout mathematics, but you are likely looking for deeper applications. For a good concrete example, I would suggest that you look into synthetic differential geometry. This is an axiomatic approach to differential geometry which takes place in a smooth topos.


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The theory is very beautiful and intuitive, and allows you to rigorously reason using infinitesimals. Since this is a purely axiomatic theory, you can come up with a variety of different models which satisfy the axioms. The ones differential geometers would be most interested in are so-called well-adapted models, where the category of smooth manifolds embeds fully and faithfully.


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  • But there are other models which would be of more interest to algebraic geometers, allowing you to use differential-geometric reasoning and tools in algebraic geometry. If you are interested in learning more, there is a freely available text by Anders Kock, who is one of the pioneers of this theory.

    Forking independence from the categorical point of view

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