
Centre (category)
Encyclopedia
Let
be a 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
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 .

Monoidal category
In mathematics, a monoidal category is a category C equipped with a bifunctorwhich is associative, up to a natural isomorphism, and an object I which is both a left and right identity for ⊗, again up to a natural isomorphism...
. The centre of




and
-
(this is actually a consequence of the first axiom).
An arrow from (A,u) to (B,v) in




The category


where
