Center (category theory)
Let be a (strict) monoidal category. The center of , also called the Drinfeld center of  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 .
- Joyal, André; Street, Ross (1991), "Tortile Yang-Baxter operators in tensor categories", Journal of Pure and Applied Algebra, 71 (1): 43–51, doi:10.1016/0022-4049(91)90039-5, MR 1107651.
- Majid, Shahn (1991). "Representations, duals and quantum doubles of monoidal categories". Proceedings of the Winter School on Geometry and Physics (Srní, 1990). Rendiconti del Circolo Matematico di Palermo. Serie II. Supplemento (26). pp. 197–206. MR 1151906.
- Drinfeld center in nLab
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