I am new in category theory. I am trying to prove the well known fact that if you have a commutative diagram of the form □□, where each square is a pullback, then the whole diagram is a pullback too, and hence deduce that the pullback of a pullback square is a pullback. Every book I have looked at has this as an exercise, but I (embarrasingly, I know) cannot see the solution. I have tried using the universality property of the two pullbacks but i am lost in calculations. If someone could help, I would really appreciate it.
How to prove the pullback lemma
4
$\begingroup$
category-theory
-
0See also [this question](http://math.stackexchange.com/q/80612). – 2012-05-30
-
1Crossposted: http://mathoverflow.net/questions/98378/very-very-elementary-lemma-on-pullbacks-which-i-just-cannot-prove – 2012-05-30
-
0You might also try posting your work up to the point where you get lost in calculations; then someone might help you find your way out again. – 2012-05-30