In a model category $\mathcal{C}$ admitting a forgetful functor to simplicial sets, is the coproduct of weak equivalences a weak equivalence?
Say even just coproducts indexed by $\mathbf{N}$.
A reference?


For example, the model category of simplicial bi-modules over a commutative rings with fibrations and weak equivalences defined to be those that are fibrations/weak equivalences of underlying simplicial sets, satisfies this, because homology of chain complexes commutes with coproducts.


However, just as an example, what about simplicial commutative monoids with analogous model structure, for instance?



Coproducts of weak equivalences
Dmitri's comment shows that the answer to your question is no. However, if you are looking at weak equivalences between cofibrant objects, then coproducts are again weak equivalences. See Lemma 4.7 in my paper on commutative monoids in general model categories: <https://arxiv.org/pdf/1403.6759.pdf>


