Subobjects of the successive power objects in the topos G-Set

Details Subobjects of the successive power objects in the topos G-Set Subobjects of the successive power objects in the topos G-Set

2006-11-27

arxiv.org/abs/math/0611821v1

Journal of Natural Geometry 11 (1997), no. 2, pp. 129-130

Mathematics

Category Theory

2 pages, LaTeX2e

Scientific paper

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 < sup{card P(M),
card P(P(M)), card P(P(P(M))),...} and {g \in G: \forall m \in M gm=m}
\subseteq {g \in G: \forall x \in X gx=x}.

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