David Roberts
weak equivalence of internal categories

If JJ is a pretopology on a category with pullbacks, a JJ-equivalence f:XYf:X \to Y between categories internal to SS is a functor that is fully faithful? and essentially JJ-surjective. This last means that the map

X 0× f,Y 0,sY 1Y 1tY 0 X_0 \times_{f,Y_0,s} Y_1 \to Y_1 \stackrel{t}{\to} Y_0

admits local sections with respect to JJ.

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.