Examples of categorification
Louis Crane, David N. Yetter
TL;DR
This paper constructs tensor and bitensor categories with specified fusion algebra structures to provide test cases for 4-D TQFT conjectures and explore related topological quantum field theory constructions.
Contribution
It offers explicit examples of categories with given Grothendieck rings, aiding the testing of Crane-Frenkel 4-D TQFT conjectures and other TQFT constructions.
Findings
Constructed tensor and bitensor categories with specified fusion rules
Provided examples to test 4-D TQFT conjectures
Enhanced understanding of categorical structures in TQFTs
Abstract
We construct tensor and bitensor categories with given Grothedieck rig (fusion algebra) in simple cases. The results provide examples on which to test the conjectural construction of 4-D TQFT's proposed by Crane and Frenkel and shed light on several other constructions of TQFT's.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra