TL;DR
This paper explores spherical functors between triangulated categories, providing examples, conditions for tangle representations, and a structure theorem, thereby extending the concept of spherical objects in category theory.
Contribution
It introduces spherical functors, offers conditions for tangle category representations, and proves a related structure theorem, advancing the understanding of categorical symmetries.
Findings
Examples of spherical functors are provided.
Sufficient conditions for tangle representations are established.
A structure theorem for these representations is proved.
Abstract
This paper has been withdrawn and replaced by arXiv:1309.5035. In this paper we describe some examples of so called spherical functors between triangulated categories, which generalize the notion of a spherical object. We also give sufficient conditions for a collection of spherical functors to yield a weak representation of the category of tangles, and prove a structure theorem for such representations under certain restrictions.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Mathematical Biology Tumor Growth · Digital Image Processing Techniques