In my previous reply to F. Lamarche's question, please take off from the last line of Remark 1: " (or cardinals as well) ". The site of cardinals 1, 2 also has the non-trivial involution 2 -> 2; its topos of presheaves is "INVOLUTIVE reflexive graphs" (which is also of interest in homotopy, of course). M. Grandis