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I went through the section “For internal groups actions” (here) and fixed/adjusted the wording a little. In the lead-in paragraphs I tried to clarify the cross-referencing, for ease of the reader. In particular, where it said
is itself a topos, by the same proof.
I added pointer back to Theorem 3.11 (here) – and that theorem itself I gave a lead-in sentence to indicate that it summarizes the preceding statements (for it looked like not having a proof at all).
In the Definition I have replaced the description of the morphisms as “$G$-invariant maps” by “$G$-equivariant functions” – for clarity.
(Of course the $G$-equivariant functions are the $G$-invariants in the mapping space. If that perspective is meant and felt to be crucial here, then we should make that explicit in the entry.)
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