Drinfeld Center

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.