I learned that there is a model structure on the category of simplicial rings. But one of the condition for model strucure is the exitence of (at least finite) limits and colimits. Existence of limits is easy(usual construction), but what about colimits?
Gratings for answering.
The category of simplicial rings is defined as the functor category $\operatorname{Fun}(\Delta^{\mathrm{op}}, \operatorname{Ring})$, so limits and colimits are computed pointwise. Therefore the fact that the category of simplicial rings admits limits and colimits follows from the fact that the category of rings admits those.