Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 62 for “"Category theory"”.
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Parametrized higher category theory
We develop foundations for the category theory of [infinity]-categories parametrized by a base occategory. Our main contribution is a theory of parametrized homotopy limits and colimits, which recovers and extends the Dotto-Moi theory of G-colimits for G a finite group when the base is chosen to be …
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Generic Theorem Proving Using HOL2P: A Category Theory Inspired Approach
… a formalisation and implementation of a category theory inspired approach to generic program specification. Theorems to simplify verification of generic programs are developed along with a formal framework for reasoning. The result is theorem proving support based on type quantification …
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Formal ᴘ‑Category Theory and Normalisation for Simple Type Theory
This thesis extends ᴘ‑category theory, introduced in Čubrić et al. (1998), and develops ᴘ‑bicategory theory, and thereafter uses them to conduct a ᴘ‑categorical analysis and synthesis of normalisation by evaluation for simple type theory. ᴘ‑category theory was introduced as a non-standard …
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Categories with New Foundations
While the interaction between set theory and category theory has been studied extensively, the set theories considered have remained almost entirely within the Zermelo family. Quine’s New Foundations has received limited attention, despite being the one-sorted version of a theory mentioned as a …
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Fractoids
… context for this structure, by looking at both category theory and universal algebra. We present some first basic concepts of category theory and consider F-algebras (= algebras over an endofunctor F). We will then look at algebras in the sense of universal algebra. We will examine F-algebras …
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Coverings and Descent Theory of Finite Spaces
This thesis presents the categorical Galois theory of the reflection of the category of finite topological spaces into the category of discrete finite topological spaces. This turns out to be nothing but the equivalence between the category of coverings of a connected finite topological space and …
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Surrogate optimization with algebraic notes and applications within the electromagnetics context
… the magnetoquasistatic model of Maxwell’s theory is discussed. Moreover, relevant points regarding the magnetoquasistatic model’s numerical simulation and numerical optimization are examined. The key notion surrogate optimization is thoroughly elaborated which is partitioned into three …
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FROM DG-CATEGORIES OVER K TO K-LINEAR STABLE INFINITY-CATEGORIES
… preprint to its latest version. Since then the ∞-category theory and the spectral algebraic geometry theory have made progress: therefore, we think that a reproof can be useful in make this result clearer for more mathematicians. The first four chapters are devoted to laying the groundwork for the …
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Internal enriched categories
This dissertation introduces and develops the theory of internal enriched categories, arising from the internalization of the theory of enriched categories. Given an internal monoidal category V in an ambient category E, we define the notions of V-enriched category, functor and natural …
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On the mechanics of 2-dimensional carbon allotropes
… We apply the mathematical framework of category theory to articulate the precise relation between structure and mechanics of a microscopic system in a macroscopic model domain, by maintaining the chosen molecular properties across a multitude of length scales, from the nanoscale to the …
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Ternary derivations of triangular algebras
… derivations of triangular algebras. We use category theory to approach our study of ternary derivations, while also offering some straightforward computational proofs. Furthermore, we investigate some related maps, called ternary automorphisms and generalised derivations, an intermediary …
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L-Fuzzy Relations in Coq
… give an overview of lattices, L-fuzzy relations, category theory and dependent type theory before describing our implementation. In addition, we provide examples of program executions based on our framework.
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Vietoris–Rips metric thickenings and Wasserstein spaces
… metric geometry, optimal transport, and category theory. Using the geodesic structure of Wasserstein space we give a novel proof of Hausmann's theorem for Vietoris–Rips metric thickenings. We also prove the first Morse lemma in Wasserstein space and relate it to the geodesic perspective. …
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On the local and global properties of information manifolds
… manifolds, we exhibit some of the necessary category theory required to effect a discussion of homological algebra in a general setting.
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Investigations into the categorical foundations of homotopy theory
… of the categorical foundations of homotopy theory, and to illuminate some aspects of category theory by showing the role played by the formation or quotient categories in many parts of general theory. Chapter 1 defines and classifies various types of quotient functor and gives methods of …
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A computational approach to higher categories
… generally, manifold diagrams. It implements the theory of associative n-categories, which is a semistrict model of higher categories. The terms of the theory, called n-diagrams, are defined inductively and have a direct representation as manifold diagrams. The tool allows users to construct and …
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Parameterized monads in linguistics
… monads, a particular theoretical framework in category theory, as a dynamic semantic framework to reinterpret the compositional Discourse Representation Theory(cDRT), and to provide an analysis of donkey anaphora. Parameterized monads are also used in this dissertation to interpret information …
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The pullback closure, perfect morphisms and completions
… to abstract categories. The categorical theory of factorisation structures for families of morphisms which developed in the 1970's laid the foundation for an axiomatic theory of categorical closure operators. This theory drew together many endeavours involving closure operations, and was …
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Mapping spatial relations
… world. In this thesis, I present a computational theory for how spatial relations are grounded in the perceptual world. Three constraints are critical to this theory: abstractness, groundedness and flexibility all of which need to be satisfied in order to explain the structure of spatial concepts. …
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