Hello, First of all sorry for the beginner's question. I have been reading various sources about the notion of a subobject classifier, e.g. McClarty's book, Lawvevre's book. Let assume the following situation: 1) Has a subobject classifier, true : 1 ---------> Omega. 2) Have an object X and object A and a monomorphism subX: A------->X. 3) With 2), we will have the pullback diagram with the corners of the pullback being the subobject classifier and the unqiue classifier/classifier X------>Omega 4)We have either a element, el: 1------>X or a generalized el: element H------->X. Question: Let's assume for simplicity that our category is Set. The problem is I don't understand how the notion of a subobject classifier determines whether "el" does or does not belong to the aforementioned subobject, "subX"! (I know that the outer commuting square figures in this, but it seems like every element will be "classified" as belonging to "subX"). Thanks and regards, Bill Halchin 20-Aug-2001 18:17:23 -0300,1833;000000000000-00000011