If is a pretopology on a category with pullbacks, a -equivalence between categories internal to is a functor that is fully faithful? and essentially -surjective. This last means that the map
admits local sections with respect to .
When no reference to a particular pretopology is mentioned, such maps will be called weak eqivalences
Created on March 31, 2009 at 23:28:01. See the history of this page for a list of all contributions to it.