Let $\mathbb{T}$ be a finitary algebraic theory and $\mathbb{T}\text{-Alg(Set)}$ be the category of finite-product-preserving functors $\mathbb{T} \rightarrow \text{Set}$.
It is written in my textbook that "It is known that the category $\mathbb{T}\text{-Alg(Set)}$ is complete and cocomplete."
I want to prove this. I can prove the completeness, since its limits are pointwise limit. However, the coproduct isn't pointwise coproduct.
How do you prove the cocompleteness?