Jason Parker - Covariant Isotropy of Grothendieck Toposes
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 2021-07-01

Talk at the school and conference “Toposes online” (24-30 June 2021):
https://aroundtoposes.com/toposesonline/

Slides:
https://aroundtoposes.com/wp-content/uploads/2021/07/ParkerSlidesToposesOnline.pdf

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.