Accessible categories with limits of some class

Giacomo Tendas – 5 August 2020

It is well known, since Gabriel and Ulmer, that an accessible category is complete if and only if it is cocomplete. In the same fashion, Diers proved that an accessible category has connected limits if and only if it is multi-cocomplete. Similar characterisation have been also given for accessible categories with products and with wide pullbacks. The aim of this talk is to recover these (and provide new) examples as part of a general setting.