The example from Philip Ehlers is interesting and, although I haven't checked it, I presume it is correct. On the other hand, my last posting is also right (and his example fails it too). And I _do_ remember being told that a complex is Kan iff homotopy is an ER. So what gives? Well, way back when I studied algebraic topology, we were told that two k simplexes in a SS were homotopy if there was an n-simplex (n > k) of which they were faces. Then homotopy of simplexes is the ER generated by this. Now when you triangulate a square (that is, I x I) you get two triangles, so that, for example, two 1-simplexes are homotopic, by the reln that Ehlers used, if there are a pair of simplexes with a common edge of which these are faces of the one and the other. Of course, these generate the same ER, but they are not the same ER and it is possible for one, but not the other, to be an ER. Michael ======================================