This is about $\S II.5$ of Mac Lane and Moerdijk's, "Sheaves in Geometry and Logic [. . .]" and is a follow-up to this: Just what is Mac Lane & Moerdijk's $\Lambda$ from $\S II.5$?
The Question:
What is Mac Lane and Moerdijk's $\Gamma$ in $\S II.5$?
Thoughts:
I'm at a loss on:
What the domain of $\Gamma$ is.
What the codomain of $\Gamma$ is.
(I'm guessing it's ${\rm Sh}(X)$.)
What $\Gamma$ does to the objects in its domain.
What $\Gamma$ does to the arrows in its domain.
So . . . Basically everything. (Sorry!)
When I read $\S II.5$ for the first time, I had an illusory sense of understanding that has now buckled under further investigation.
It appears that $\Gamma$ is defined in terms of its relationship to $\Lambda$, something I have only a rudimentary grasp of.
I need to understand $\Gamma$ in order to do Exercise II.6.
Please help :)