The other pullback lemma
arXiv:1311.2974
Abstract
Given a composition of two commutative squares, one well-known pullback lemma says that if both squares are pullbacks, then their composition is also a pullback; another well-known pullback lemma says that if the composed square is a pullback and the supporting square is a pullback, then the other square is a pullback as well. This note investigates the third of the possibilities.