# Pointed Drinfeld Center Functor

@article{Kong2019PointedDC, title={Pointed Drinfeld Center Functor}, author={Liang Kong and Wei Yuan and Hao Zheng}, journal={Communications in Mathematical Physics}, year={2019}, volume={381}, pages={1409-1443} }

In this work, using the functoriality of the Drinfeld center of fusion categories, we generalize the functoriality of the full center of simple separable algebras in a fixed fusion category to all fusion categories. This generalization produces a new center functor, which involves both Drinfeld center and full center and is called pointed Drinfeld center functor. We prove that this pointed Drinfeld center functor is a symmetric monoidal equivalence. It turns out that this functor provides a…

## 7 Citations

### A mathematical theory of gapless edges of 2d topological orders. Part I

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### The Symmetry Enriched Center Functor is Fully Faithful

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In this work, inspired by some physical intuitions, we define a series of symmetry enriched categories to describe symmetry enriched topological (SET) orders, and define a new tensor product, called…

### Categories of quantum liquids I

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We develop a mathematical theory of separable higher categories based on Gaiotto and Johnson-Freyd’s work on condensation completion. Based on this theory, we prove some fundamental results…

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## References

SHOWING 1-10 OF 47 REFERENCES

### Boundary-bulk relation for topological orders as the functor mapping higher categories to their centers

- Mathematics
- 2015

In this paper, we study the relation between topological orders and their gapped boundaries. We propose that the bulk for a given gapped boundary theory is unique. It is actually a consequence of a…

### Fusion categories and homotopy theory

- Mathematics
- 2009

We apply the yoga of classical homotopy theory to classification problems of G-extensions of fusion and braided fusion categories, where G is a finite group. Namely, we reduce such problems to…

### On fusion categories

- Mathematics
- 2002

Using a variety of methods developed in the literature (in particular, the theory of weak Hopf algebras), we prove a number of general results about fusion categories in characteristic zero. We show…

### Finite tensor categories

- Mathematics
- 2003

We start the general structure theory of not necessarily semisimple finite tensor categories, generalizing the results in the semisimple case (i.e. for fusion categories), obtained recently in our…

### A mathematical theory of gapless edges of 2d topological orders. Part I

- Physics, MathematicsJournal of High Energy Physics
- 2020

This is the first part of a two-part work on a unified mathematical theory of gapped and gapless edges of 2d topological orders. We analyze all the possible observables on the 1+1D world sheet of a…

### Monoidal categories in, and linking, geometry and algebra

- Mathematics
- 2012

This is a report on aspects of the theory and use of monoidal categories. The first section introduces the main concepts through the example of the category of vector spaces. String notation is…