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 .
Famous quotes containing the word centre:
“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 (18031882)