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

and

(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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    Belief and love,—a believing love will relieve us of a vast load of care. O my brothers, God exists. There is a soul at the centre of nature, and over the will of every man, so that none of us can wrong the universe.
    Ralph Waldo Emerson (1803–1882)