Exercise 2, § 1

Let us take up again the notations of the prop. 7 of I, p. 15.

a) Give an example where the squares (12) and (14) are Cartesian, but where the square (13) is not.

b) Suppose that the mapping $f\circ g$ is surjective and universally strict. Prove that if two of the squares (12), (13) and (14) are Cartesian, the third is also. (Use Exercise 1.)