Exercise 1.7.17 (Pasting lemma for pullback squares). Consider a commutative diagram

Commutative diagram generated from the LaTeX source

If the right-hand square is a pullback square, then the left-hand square is a pullback square if and only if the outer rectangle is a pullback square. Hint: compare with Lemma 1.3.15.

Generated from the authoritative LaTeX source.