Centre (category)

Let be a (strict) monoidal category. The centre of , 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 .

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