Suppose whole square and the left square in the diagram below are pullbacks, then we may wonder whether the right square is a pullback. It is usually not the case. 

Now we seek some addition condition on $X\to Y$ that forces the right square is a pullback too. 

My question: is epic a sufficient condition? (If the category is Sets, then yes.)


![square][1]


  [1]: https://i.sstatic.net/yhrcd.jpg