Kock A. and G. E. Reyes (1999). Aspects of fractional exponent functor. Theory Appl. Categ. 5, No. 10, 251-265. (Electronic)

We prove that certain categories arising from atoms in a Grothendieck topos are themselves Grothendieck toposes. We also investigate enrichments of these categories over the base topos; there are in fact often two distinct enrichments.

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