Subobjects of the successive power objects in the topos G-Set
Abstract
Let G be a group and let M be an object of the topos G-Set. We prove that an object X of the category G-Set is isomorphic to some subobject of one of the objects P(M), P(P(M)), P(P(P(M))),... if and only if card X < supcard P(M), card P(P(M)), card P(P(P(M))),... and g ∈ G: ∀ m ∈ M gm=m ⊂eq g ∈ G: ∀ x ∈ X gx=x.
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