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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?

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