I want to prove that $\text{Sh}(C_{\mathbb{T}},J)$ is the classifing topos for the theory of $\mathbb{T}$-local algebras.

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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?