Higher Gauge Theory on the Lattice
Higher Gauge Theory on the Lattice
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Date
2019-10-20
Auteurs
BOUZID Badreddine
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Éditeur
Université Oran1 Ahmed Ben Bella
Résumé
The aim of this thesis is two-fold. First, we give a detailed presentation of higher structures involved in the higher gauge theory, this is done progressively by recalling the basic definitions of category theory, then using enrichment and internalization processes to define the higher structures, finally we apply these processes to define the higher analogous of the transition functions for a fiber bundle. Second, we use calculus on the lattice to prove the transition laws for these higher transition functions, results found on the first part of this thesis will be widely used to achieve these calculations.
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Mots-clés
Higher gauge theory, Higher category theory, 2-connection, Lattice, 2-transition laws, 2-holonomy, 2-bundles, Enrichment, Internalization, 2-group