Center (category theory)

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Let be a (strict) monoidal category. The center of , also called the Drinfeld center of [1] and denoted , is the category whose objects are pairs (A,u) consisting of an object A of and a natural isomorphism satisfying


(this is actually a consequence of the first axiom).

An arrow from (A,u) to (B,v) in consists of an arrow in such that


The category becomes a braided monoidal category with the tensor product on objects defined as

where , and the obvious braiding .