Exercise 1.3.14 (Iterated pullbacks). Consider a commutative diagram
Construct an equivalence \[ D_1 \times _{D_3} C_3 \iso D_1 \times _{D_2} (D_2 \times _{D_3} C_3). \] Hint: define one direction by \((\pr _{D_1}, (h_1 \circ \pr _{D_1}, \pr _{C_3}))\) and construct an inverse by projecting to \(D_1\) and \(C_3\).
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