Abstract
The main purpose of this talk is to abstract and generalize several known sheafification-like adjunctions for toposes (arising as instances of the tripos-to- topos construction) as “geometric” morphisms of triposes. In particular, we will focus on three specific cases: the ordinary sheafification for localic toposes, particular instances of the sheafification-like adjunction between the $ex/reg$ and the $ex/lex$ completion of a regular category, and finally the sheafification-like adjunction between Set and a realizability topos. To achieve this goal, we will combine the tripos-to-topos construction with the full existential completion and the characterization of toposes arising as $ex/lex$ completions, taking advantage of the careful 2-categorical analysis of the tripos-to-topos construction and of the presentation of such a construction in terms of exact completions. This talk is based on a joint work with Maria Emilia Maietti
Davide Trotta
Postdoc
I am a mathematician, and my research is mainly focused on categorical logic and its applications in theoretical computer science.