In his answer to [this][1] MO question, Karl Schwede claimed that every non-normal variety can be obtained by an appropriate pushout diagram, as sketched in that answer. This would give substance to the heuristics according to which "a normal variety is a variety that has no undue gluing of subvarieties or tangent spaces" (again, see K.Schwede's answer and the examples therein).

**Q.** Has a proof of that fact been written down somewhere since then? If yes, where? And if not, could anybody who knows it sketch it here on MO?




  [1]: https://mathoverflow.net/questions/109395/is-there-a-geometric-intuition-underlying-the-notion-of-normal-varieties