Skeletonization Of Fusion Categories
In mathematics, the skeletonization of fusion categories is a process whereby one extracts the core data of a fusion category or related categorical object in terms of minimal Set theory, set-theoretic information. This set-theoretic information is referred to as the skeletal data of the fusion category. This process is related to the general technique of Skeleton (category theory), skeletonization in category theory. Skeletonization is often used for working with examples, doing computations, and classifying fusion categories. The relevant feature of Fusion category, fusion categories which makes the technique of skeletonization effective is the strong finiteness conditions placed on fusion categories, such as the requirements that they have finitely many isomorphism classes of Schur's lemma, simple objects and that all of their Hom space, hom-spaces are finite dimensional. This allows the entire categorical structure of a fusion category to be encoded in a finite amount of complex ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]