Grothendieck topology on functor category

Question

Let $A$ be a ring. Denote by $A-\text{Psh}$ the category of covariant functors $X : A-\text{Alg} \to \text{Set}$ the question is : Can i define a Grothendieck topology on $A-\text{Psh}$ by descrybing directly the sheaf ;

An idempotent sheaf is a functor $X : A-\text{Alg} \to \text{Set}$ such that for all $A$-algebra $R$ for all $(e_1,\dots,e_n) \in R^n$ such that

1. for $i \ne j$, $e_i e_j = 0$
2. for all $i$, $e_i^2 = e_i$
3. $\sum e_i = 1$

for all, $\zeta_1,\dots, \zeta_n$, with $ \zeta_i \in X(R[e_i^{-1}])$ there is an unique $\zeta \in X(R)$ such that : for all $i$ : $$ \zeta = \zeta_i \text{ in }X(R[e_i^{-1}]) $$

I ask the gluing Zariski condition but only for idempotent covering.