Let $\mathbb{T}$ be a essentially algebraic theory, $C_{\mathbb{T}}$ be its syntactic category and $J$ be a subcanonical coverage on $C_{\mathbb{T}}$
Then, I want to understand why "$\text{Sh}(C_{\mathbb{T}},J)$ is the classifing topos for the geometric theory of $\mathbb{T}$-local algebras."(nlab)
Where should I start from?
I know the definition of geometric theory, essential algebraic theory, subcanonical coverage, grothendieck topos, etc... but don't know how to construct "geometric theory of $\mathbb{T}$-local algebras" and why $C_{\mathbb{T}} \simeq \mathbb{T}\text{Alg}^{\text{fp}}$ holds. I'm unfamiliar with syntactic category.
Could you recommend some literature?