Weakly Terminal Objects in Quasicategories of $mathbb{SET}$ Endofunctors

摘要

The quasicategory ℚ of all set functors (i.e. endofunctors of the category $mathbb{SET}$ of all sets and mappings) and all natural transformations has a terminal object – the constant functor C 1. We construct here the terminal (or at least the smallest weakly terminal object, which is rigid) in some important subquasicategories of ℚ – in the quasicategory $mathbb{F}$ of faithful connected set functors and all natural transformations, and in the quasicategories $mathbb{B}^{(kappa)}$ of all set functors and natural transformations which preserve filters of points (up to cardinality κ).