Colimits in Topoi

Abstract

Given a cartesian closed category E with subobject classifier t:l-*Q, it is shown that the functor Q ( ) : E 0V ->E is tripleable. Standard results from the theory of triples are then used to show that E has /-colimits if and only if it has 7 op -limits. This gives a new proof of Mikkelsen's theorem which states that E has all finite colimits.