##  [Drinfeld Center](/drinfeld-center) 

  ##  [Drinfeld Center](https://algebra.quantumdictionary.io/drinfeld-center-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

For a monoidal category C, the Drinfeld center Z(C) (also called the categorical center) is the category whose objects are pairs (Z, γ_{Z,-}) where Z ∈ C and γ_{Z,X}: Z ⊗ X ≅ X ⊗ Z is a natural family of isomorphisms (a half-braiding) satisfying coherence (hexagon) conditions; Z(C) is braided and universal among braided categories receiving a monoidal functor from C.