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Created the page Fraenkel-Mostowski model and populated it with basic definitions and information moved from ZFA
There are already entries for Schanuel topos and nominal set.
In the category-theoretic approach (moved from the previous ZFA page), do we have to require the each element of the sets to have an open stabilizer? This would correspond to requiring the sets in the classical permutation model to be hereditarily symmetric, rather than just being symmetric.
do we have to require the each element of the sets to have an open stabilizer?
Depends what you are needing. Maybe I was thinking of symmetric models at the same time if it was me that wrote it (I guess I did).
If we take a set in a permutation model, then it’s elements would have open stabilizers, so I believe this should be reflected in the corresponding category. This also corresponds to the action of the group being continuous (if the set is given the discrete topology), which is by itself a natural thing to require if we are given a topological group.
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