# What are $(S,\Sigma)$-CCCs?

I was reading this and I was trying to understand the definition of $$(S,\Sigma)$$-CCC. The first requirement says:

a mapping [[_]] : S → |C|, associating some object [[s]] ∈ |C| to any s ∈ S;

which I find very confusing and having a hard time understanding what it means. What is $$S$$ and what is $$\Sigma$$?

why do all the other requirements mean intuitively?