Geodesic
Double power monad preserving adjunctions are Frobenius
Theory and applications of categories, Tome 33 (2018), pp. 476-491.

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We give a direct proof that between two toposes, F and E, bounded over a base topos S, adjunctions L -| R: Loc_F -> Loc_E over Loc_S are Frobenius if and only if R commutes with the double power locale monad and finite coproducts. The proof uses only certain categorical properties of the category of locales, Loc. This implies that between categories axiomatized to behave like categories of locales, it does not make a difference whether maps are defined as structure preserving adjunctions (i.e. those that commute with the double power monads) or Frobenius adjunctions.
Publié le :
Classification : 06D22, 18D35, 18B40, 22A22
Keywords: topos, locale, geometric morphism, Frobenius reciprocity, power monad 
@article{TAC_2018_33_a16,
     author = {Christopher Townsend},
     title = {Double power monad preserving adjunctions are {Frobenius}},
     journal = {Theory and applications of categories},
     pages = {476--491},
     publisher = {mathdoc},
     volume = {33},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2018_33_a16/}
}
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Christopher Townsend. Double power monad preserving adjunctions are Frobenius. Theory and applications of categories, Tome 33 (2018), pp. 476-491. http://geodesic.mathdoc.fr/item/TAC_2018_33_a16/