If M a monoid and $Set^M$ a topos associate to M, I found $Set^M$ have (epi, strong,mono) factorization system([http://math.stackexchange.com/questions/541300/epi-mono-factorization-in-presentable-categories][1]), I think $Set^M$ has (epi,mono source) factorization [\[http://katmat.math.uni-bremen.de/acc/acc.pdf][2], pag. 257]  but I can not found the proof of that, I would like see some reference of the proof such that don't use the fact $Set^M$ is a locally presentable category or If I suppose it's wrong a liked see the counterexample.


  [1]: http://math.stackexchange.com/questions/541300/epi-mono-factorization-in-presentable-categories
  [2]: http://katmat.math.uni-bremen.de/acc/acc.pdf