PlanetPhysics/Center of Abelian Category

Let $𝒜$ be an [[../AbelianCategory2/|abelian category]]. Then one also has the identity morphism (or identity functor) $i{d}_{𝒜}:𝒜\to 𝒜$. One defines the center of the Abelian category Failed to parse (syntax error): {\displaystyle \mathcal{A } } by $Z(𝒜)=End(i{d}_{𝒜}).$

One can show that the center is $Z(CohX)\cong 𝒪((X)$ for any [[../IsomorphismClass/|algebraic variety]] where $𝒪(X)$ is the ring of global [[../CoIntersections/|regular]] [[../Bijective/|functions]] on $X$ and $𝐂oh(X)$ is the Abelian category of coherent sheaves over $X$.

One can show also prove the following lemma. \begin{theorem} {\mathbf Associative Algebra Lemma}

If $A$ is a associative algebra then its center $Z(A-mod)=ZA.$ \end{theorem}