Appears in collection : Toposes Online

Covariant isotropy can be regarded as providing an abstract notion of conjugation or inner automorphism for an arbitrary category. After reviewing the characterization of covariant isotropy in locally presentable categories (regarded as categories of models of essentially algebraic theories), we characterize the covariant isotropy of any Grothendieck topos, showing that it essentially agrees with the previously obtained characterization of covariant isotropy for presheaf toposes.