“Biased elementary doctrines and generalized quotient completion”
Lunedì 27 Giugno 2022, ore 15:00 - Aula 2AB45 - Cipriano Cioffo (Università di Milano)
In this talk I will present the framework of the biased elementary doctrines. These objects provide a generalization of the notion of elementary doctrine introduced by Maietti and Rosolini, which consists of a suitable functor from a category with finite products to the category of posets and monotone functions. The main novelty is that for a biased elementary doctrine the domain category may lack finite products. Moreover, for these structures I will introduce a notion of quotient completion which generalizes the elementary quotient completion. Along the way, I will discuss the motivations that led to the introduction of this framework and two main examples of biased elementary doctrines, one of which coming from type theory.