I want to show that simplicial abelian sheaves are fibrant. For this, I wonder whether a morphism between simplicial sheaves is a fibration iff it has RLP w.r.t. all morphisms like $$\Lambda^n_k\times X\to\triangle^n\times X$$ where $X\in Sm/k$. Is this claim true?

I want to show that simplicial abelian sheaves are fibrant. For this, I wonder whether a morphism between simplicial sheaves is a fibration iff it has RLP w.r.t. all morphisms like $$\Lambda^n_k\times X\to\triangle^n\times X$$ where $X\in Sm/k$. Is this claim true?

Here weak equivalences are stalkwise weak equivalences and cofibrations are monomorphisms.