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Question about "Free-ness" of Free SCWF

The way to get a "free" functor rather than an initial object is to allow the $\mathcal B$ in the category $\mathcal B$-Scwfs to vary. Then there is a forgetful functor $U$ from the category ...
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Question in relating STLC and Free CCC

If you start out with a graph $1 \rightrightarrows 2$, then what you get is not the $2$ you'd expect. The result would be equivalent to (in the resulting logic): ...
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