Definition 0.1. Let 𝒜 be an Abelian category. Then one also has the identity morphism
(or identity functor) id𝒜 : 𝒜→𝒜. One defines the center of the Abelian category 𝒜 by
Example 0.1. One can show that the center is Z(CohX)
𝒪((X) for any algebraic variety
where 𝒪(X) is the ring of global regular functions on X and Coh(X) is the Abelian category
of coherent sheaves over X.
One can show also prove the following lemma.
Theorem 0.1. Associative Algebra Lemma
If A is a associative algebra then its center
