Apart from usual examples of toposes, I'd like to know if some of the following categories and some of their subcategories are known to be toposes :

  • the category $\text{Heyt}$ of Heyting algebras and morphisms between them (and subcategories like the category $\text{CHeyt}$ of complete Heyting algebras),

  • the category $\text{Loc}$ of locales and morphisms between them,

  • the category $\text{Frm}$ of frames and morphisms between them ($\text{Loc}=\text{Frm}^{\text{op}}$),

  • the category $\text{Bool}$ of boolean algebras).

Edit : and what about the category $\text{Stone}$ of Stone spaces ?

  • 8
    $\begingroup$ None of the above: all of these categories are not even cartesian closed. $\endgroup$ – Zhen Lin Nov 23 '13 at 13:26

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