# ct.category theory – tensor triangulated categories

Let $$(mathcal{T},otimes)$$ be a monoidal (not necessarily symmetric and possibly without unit object) triangulated category where $$-otimes-$$ is exact on both variables. Let $$S$$ be a set of objects in $$mathcal{T}$$ such that for any $$s_1in S$$ and $$s_2in S$$ we have that $$s_1otimes s_{2}in S$$.

I was wondering if the thick subcategory generated by $$S$$ is automatically monoidal?