Everyone is like "Sephiroth was brought back to life," but I have another theory. Many people seem to (possibly wrongly) interpret that Sephiroth took the place of Kadaj. However, after watching the movies (both normal and complete) a number of times, it seems more like Seph's soul/spirit/whatever got into Kadaj. It was still Kadaj, only with the appearance of Sephiroth. Because, even with such a work of fiction, having a character come back from the dead, make someone else completely disappear (and conveniently bring him back when he dies) doesn't seem right.
That's another point of view worth looking into.